id	sid	tid	token	lemma	pos
ap-9258	1	1	acta	acta	PROPN
ap-9258	1	2	polytechnica	polytechnica	PROPN
ap-9258	1	3	https://doi.org/10.14311/ap.2024.64.0470	https://doi.org/10.14311/ap.2024.64.0470	PROPN
ap-9258	1	4	acta	acta	PROPN
ap-9258	1	5	polytechnica	polytechnica	PROPN
ap-9258	1	6	64(5):470–486	64(5):470–486	NUM
ap-9258	1	7	,	,	PUNCT
ap-9258	1	8	2024	2024	NUM
ap-9258	1	9	©	©	ADP
ap-9258	1	10	2024	2024	NUM
ap-9258	1	11	the	the	DET
ap-9258	1	12	author(s	author(s	NOUN
ap-9258	1	13	)	)	PUNCT
ap-9258	1	14	.	.	PUNCT
ap-9258	2	1	licensed	license	VERB
ap-9258	2	2	under	under	ADP
ap-9258	2	3	a	a	DET
ap-9258	2	4	cc	cc	NOUN
ap-9258	2	5	-	-	PUNCT
ap-9258	2	6	by	by	ADP
ap-9258	2	7	4.0	4.0	NUM
ap-9258	2	8	licence	licence	NOUN
ap-9258	2	9	published	publish	VERB
ap-9258	2	10	by	by	ADP
ap-9258	2	11	the	the	DET
ap-9258	2	12	czech	czech	PROPN
ap-9258	2	13	technical	technical	PROPN
ap-9258	2	14	university	university	PROPN
ap-9258	2	15	in	in	ADP
ap-9258	2	16	prague	prague	PROPN
ap-9258	2	17	acoustic	acoustic	ADJ
ap-9258	2	18	radiation	radiation	NOUN
ap-9258	2	19	beam	beam	NOUN
ap-9258	2	20	patterns	pattern	NOUN
ap-9258	2	21	of	of	ADP
ap-9258	2	22	different	different	ADJ
ap-9258	2	23	polygonal	polygonal	ADJ
ap-9258	2	24	piston	piston	NOUN
ap-9258	2	25	surfaces	surface	NOUN
ap-9258	2	26	taofeek	taofeek	VERB
ap-9258	2	27	ayotunde	ayotunde	PROPN
ap-9258	2	28	yusufa,∗	yusufa,∗	PROPN
ap-9258	2	29	,	,	PUNCT
ap-9258	2	30	sheriff	sheriff	PROPN
ap-9258	2	31	abiodun	abiodun	PROPN
ap-9258	2	32	aodub	aodub	PROPN
ap-9258	2	33	,	,	PUNCT
ap-9258	2	34	abeeb	abeeb	PROPN
ap-9258	2	35	opeyemi	opeyemi	NOUN
ap-9258	2	36	alabib	alabib	NOUN
ap-9258	2	37	a	a	DET
ap-9258	2	38	joseph	joseph	PROPN
ap-9258	2	39	sarwuan	sarwuan	PROPN
ap-9258	2	40	tarka	tarka	PROPN
ap-9258	2	41	university	university	PROPN
ap-9258	2	42	,	,	PUNCT
ap-9258	2	43	mechanical	mechanical	ADJ
ap-9258	2	44	engineering	engineering	NOUN
ap-9258	2	45	department	department	PROPN
ap-9258	2	46	,	,	PUNCT
ap-9258	3	1	p.	p.	PROPN
ap-9258	3	2	m.	m.	PROPN
ap-9258	3	3	b.	b.	PROPN
ap-9258	3	4	2373	2373	NUM
ap-9258	3	5	,	,	PUNCT
ap-9258	3	6	970101	970101	NUM
ap-9258	3	7	makurdi	makurdi	NOUN
ap-9258	3	8	,	,	PUNCT
ap-9258	3	9	nigeria	nigeria	PROPN
ap-9258	3	10	b	b	PROPN
ap-9258	3	11	kyungpook	kyungpook	PROPN
ap-9258	3	12	national	national	PROPN
ap-9258	3	13	university	university	PROPN
ap-9258	3	14	,	,	PUNCT
ap-9258	3	15	school	school	NOUN
ap-9258	3	16	of	of	ADP
ap-9258	3	17	mechanical	mechanical	ADJ
ap-9258	3	18	engineering	engineering	NOUN
ap-9258	3	19	,	,	PUNCT
ap-9258	3	20	daehak	daehak	PROPN
ap-9258	3	21	-	-	PUNCT
ap-9258	3	22	ro	ro	NOUN
ap-9258	3	23	80	80	NUM
ap-9258	3	24	,	,	PUNCT
ap-9258	3	25	41566	41566	NUM
ap-9258	3	26	daegu	daegu	NOUN
ap-9258	3	27	,	,	PUNCT
ap-9258	3	28	south	south	PROPN
ap-9258	3	29	korea	korea	PROPN
ap-9258	4	1	∗	∗	VERB
ap-9258	4	2	corresponding	correspond	VERB
ap-9258	4	3	author	author	NOUN
ap-9258	4	4	:	:	PUNCT
ap-9258	4	5	yustaofeekay@yahoo.com	yustaofeekay@yahoo.com	X
ap-9258	5	1	abstract	abstract	ADJ
ap-9258	5	2	.	.	PUNCT
ap-9258	6	1	transducers	transducer	NOUN
ap-9258	6	2	are	be	AUX
ap-9258	6	3	used	use	VERB
ap-9258	6	4	in	in	ADP
ap-9258	6	5	acoustic	acoustic	ADJ
ap-9258	6	6	remote	remote	ADJ
ap-9258	6	7	sensing	sensing	NOUN
ap-9258	6	8	and	and	CCONJ
ap-9258	6	9	several	several	ADJ
ap-9258	6	10	other	other	ADJ
ap-9258	6	11	modern	modern	ADJ
ap-9258	6	12	applications	application	NOUN
ap-9258	6	13	.	.	PUNCT
ap-9258	7	1	the	the	DET
ap-9258	7	2	radiating	radiate	VERB
ap-9258	7	3	surface	surface	NOUN
ap-9258	7	4	geometry	geometry	NOUN
ap-9258	7	5	of	of	ADP
ap-9258	7	6	a	a	DET
ap-9258	7	7	single	single	ADJ
ap-9258	7	8	acoustic	acoustic	ADJ
ap-9258	7	9	transducer	transducer	NOUN
ap-9258	7	10	affects	affect	VERB
ap-9258	7	11	its	its	PRON
ap-9258	7	12	beam	beam	NOUN
ap-9258	7	13	pattern	pattern	NOUN
ap-9258	7	14	and	and	CCONJ
ap-9258	7	15	has	have	VERB
ap-9258	7	16	a	a	DET
ap-9258	7	17	cumulative	cumulative	ADJ
ap-9258	7	18	effect	effect	NOUN
ap-9258	7	19	on	on	ADP
ap-9258	7	20	the	the	DET
ap-9258	7	21	overall	overall	ADJ
ap-9258	7	22	performance	performance	NOUN
ap-9258	7	23	of	of	ADP
ap-9258	7	24	an	an	DET
ap-9258	7	25	array	array	NOUN
ap-9258	7	26	configuration	configuration	NOUN
ap-9258	7	27	.	.	PUNCT
ap-9258	8	1	in	in	ADP
ap-9258	8	2	addition	addition	NOUN
ap-9258	8	3	,	,	PUNCT
ap-9258	8	4	the	the	DET
ap-9258	8	5	transducers	transducer	NOUN
ap-9258	8	6	with	with	ADP
ap-9258	8	7	polygon	polygon	NOUN
ap-9258	8	8	radiating	radiate	VERB
ap-9258	8	9	surfaces	surface	NOUN
ap-9258	8	10	provide	provide	VERB
ap-9258	8	11	more	more	ADJ
ap-9258	8	12	compact	compact	ADJ
ap-9258	8	13	structure	structure	NOUN
ap-9258	8	14	in	in	ADP
ap-9258	8	15	an	an	DET
ap-9258	8	16	array	array	NOUN
ap-9258	8	17	than	than	ADP
ap-9258	8	18	the	the	DET
ap-9258	8	19	circular	circular	ADJ
ap-9258	8	20	pistons	piston	NOUN
ap-9258	8	21	due	due	ADP
ap-9258	8	22	to	to	ADP
ap-9258	8	23	their	their	PRON
ap-9258	8	24	flat	flat	ADJ
ap-9258	8	25	surface	surface	NOUN
ap-9258	8	26	edges	edge	NOUN
ap-9258	8	27	.	.	PUNCT
ap-9258	9	1	however	however	ADV
ap-9258	9	2	,	,	PUNCT
ap-9258	9	3	until	until	ADP
ap-9258	9	4	now	now	ADV
ap-9258	9	5	,	,	PUNCT
ap-9258	9	6	the	the	DET
ap-9258	9	7	radiation	radiation	NOUN
ap-9258	9	8	patterns	pattern	NOUN
ap-9258	9	9	of	of	ADP
ap-9258	9	10	acoustic	acoustic	ADJ
ap-9258	9	11	polygonal	polygonal	ADJ
ap-9258	9	12	pistons	piston	NOUN
ap-9258	9	13	have	have	AUX
ap-9258	9	14	not	not	PART
ap-9258	9	15	been	be	AUX
ap-9258	9	16	exclusively	exclusively	ADV
ap-9258	9	17	studied	study	VERB
ap-9258	9	18	and	and	CCONJ
ap-9258	9	19	documented	document	VERB
ap-9258	9	20	.	.	PUNCT
ap-9258	10	1	in	in	ADP
ap-9258	10	2	this	this	DET
ap-9258	10	3	study	study	NOUN
ap-9258	10	4	,	,	PUNCT
ap-9258	10	5	the	the	DET
ap-9258	10	6	directional	directional	ADJ
ap-9258	10	7	factors	factor	NOUN
ap-9258	10	8	of	of	ADP
ap-9258	10	9	acoustic	acoustic	ADJ
ap-9258	10	10	pistons	piston	NOUN
ap-9258	10	11	with	with	ADP
ap-9258	10	12	polygonal	polygonal	ADJ
ap-9258	10	13	surfaces	surface	NOUN
ap-9258	10	14	of	of	ADP
ap-9258	10	15	three	three	NUM
ap-9258	10	16	to	to	PART
ap-9258	10	17	ten	ten	NUM
ap-9258	10	18	sides	side	NOUN
ap-9258	10	19	were	be	AUX
ap-9258	10	20	derived	derive	VERB
ap-9258	10	21	analytically	analytically	ADV
ap-9258	10	22	from	from	ADP
ap-9258	10	23	the	the	DET
ap-9258	10	24	first	first	ADJ
ap-9258	10	25	principle	principle	NOUN
ap-9258	10	26	using	use	VERB
ap-9258	10	27	the	the	DET
ap-9258	10	28	rayleigh	rayleigh	PROPN
ap-9258	10	29	integral	integral	NOUN
ap-9258	10	30	.	.	PUNCT
ap-9258	11	1	these	these	DET
ap-9258	11	2	directional	directional	ADJ
ap-9258	11	3	factors	factor	NOUN
ap-9258	11	4	were	be	AUX
ap-9258	11	5	used	use	VERB
ap-9258	11	6	to	to	PART
ap-9258	11	7	synthesise	synthesise	VERB
ap-9258	11	8	and	and	CCONJ
ap-9258	11	9	characterise	characterise	VERB
ap-9258	11	10	the	the	DET
ap-9258	11	11	radiation	radiation	NOUN
ap-9258	11	12	patterns	pattern	NOUN
ap-9258	11	13	of	of	ADP
ap-9258	11	14	the	the	DET
ap-9258	11	15	piston	piston	NOUN
ap-9258	11	16	sources	source	NOUN
ap-9258	11	17	in	in	ADP
ap-9258	11	18	comparison	comparison	NOUN
ap-9258	11	19	with	with	ADP
ap-9258	11	20	the	the	DET
ap-9258	11	21	baffled	baffled	ADJ
ap-9258	11	22	circular	circular	ADJ
ap-9258	11	23	piston	piston	NOUN
ap-9258	11	24	of	of	ADP
ap-9258	11	25	an	an	DET
ap-9258	11	26	equivalent	equivalent	ADJ
ap-9258	11	27	surface	surface	NOUN
ap-9258	11	28	area	area	NOUN
ap-9258	11	29	.	.	PUNCT
ap-9258	12	1	the	the	DET
ap-9258	12	2	rectangular	rectangular	ADJ
ap-9258	12	3	,	,	PUNCT
ap-9258	12	4	the	the	DET
ap-9258	12	5	triangular	triangular	NOUN
ap-9258	12	6	,	,	PUNCT
ap-9258	12	7	and	and	CCONJ
ap-9258	12	8	the	the	DET
ap-9258	12	9	rest	rest	NOUN
ap-9258	12	10	of	of	ADP
ap-9258	12	11	the	the	DET
ap-9258	12	12	polygons	polygon	NOUN
ap-9258	12	13	have	have	VERB
ap-9258	12	14	the	the	DET
ap-9258	12	15	same	same	ADJ
ap-9258	12	16	performance	performance	NOUN
ap-9258	12	17	with	with	ADP
ap-9258	12	18	the	the	DET
ap-9258	12	19	circular	circular	ADJ
ap-9258	12	20	piston	piston	NOUN
ap-9258	12	21	when	when	SCONJ
ap-9258	12	22	the	the	DET
ap-9258	12	23	surface	surface	NOUN
ap-9258	12	24	diameter	diameter	NOUN
ap-9258	12	25	is	be	AUX
ap-9258	12	26	not	not	PART
ap-9258	12	27	higher	high	ADJ
ap-9258	12	28	than	than	ADP
ap-9258	12	29	0.5λ	0.5λ	NOUN
ap-9258	12	30	,	,	PUNCT
ap-9258	12	31	0.28λ	0.28λ	PROPN
ap-9258	12	32	and	and	CCONJ
ap-9258	12	33	0.43λ	0.43λ	NOUN
ap-9258	12	34	,	,	PUNCT
ap-9258	12	35	respectively	respectively	ADV
ap-9258	12	36	.	.	PUNCT
ap-9258	13	1	the	the	DET
ap-9258	13	2	main	main	ADJ
ap-9258	13	3	lobe	lobe	NOUN
ap-9258	13	4	of	of	ADP
ap-9258	13	5	the	the	DET
ap-9258	13	6	acoustic	acoustic	ADJ
ap-9258	13	7	emissions	emission	NOUN
ap-9258	13	8	from	from	ADP
ap-9258	13	9	the	the	DET
ap-9258	13	10	square	square	NOUN
ap-9258	13	11	is	be	AUX
ap-9258	13	12	very	very	ADV
ap-9258	13	13	close	close	ADJ
ap-9258	13	14	to	to	ADP
ap-9258	13	15	that	that	PRON
ap-9258	13	16	of	of	ADP
ap-9258	13	17	the	the	DET
ap-9258	13	18	circular	circular	ADJ
ap-9258	13	19	piston	piston	NOUN
ap-9258	13	20	whose	whose	DET
ap-9258	13	21	diameter	diameter	NOUN
ap-9258	13	22	is	be	AUX
ap-9258	13	23	greater	great	ADJ
ap-9258	13	24	than	than	ADP
ap-9258	13	25	a	a	DET
ap-9258	13	26	wavelength	wavelength	NOUN
ap-9258	13	27	while	while	SCONJ
ap-9258	13	28	that	that	PRON
ap-9258	13	29	of	of	ADP
ap-9258	13	30	the	the	DET
ap-9258	13	31	rectangle	rectangle	NOUN
ap-9258	13	32	is	be	AUX
ap-9258	13	33	wider	wide	ADJ
ap-9258	13	34	.	.	PUNCT
ap-9258	14	1	the	the	DET
ap-9258	14	2	results	result	NOUN
ap-9258	14	3	show	show	VERB
ap-9258	14	4	that	that	SCONJ
ap-9258	14	5	the	the	DET
ap-9258	14	6	radiating	radiate	VERB
ap-9258	14	7	surface	surface	NOUN
ap-9258	14	8	perimeter	perimeter	NOUN
ap-9258	14	9	and	and	CCONJ
ap-9258	14	10	symmetry	symmetry	NOUN
ap-9258	14	11	are	be	AUX
ap-9258	14	12	the	the	DET
ap-9258	14	13	two	two	NUM
ap-9258	14	14	most	most	ADV
ap-9258	14	15	critical	critical	ADJ
ap-9258	14	16	factors	factor	NOUN
ap-9258	14	17	affecting	affect	VERB
ap-9258	14	18	the	the	DET
ap-9258	14	19	beam	beam	NOUN
ap-9258	14	20	characteristics	characteristic	NOUN
ap-9258	14	21	of	of	ADP
ap-9258	14	22	a	a	DET
ap-9258	14	23	piston	piston	NOUN
ap-9258	14	24	source	source	NOUN
ap-9258	14	25	rather	rather	ADV
ap-9258	14	26	than	than	ADP
ap-9258	14	27	the	the	DET
ap-9258	14	28	surface	surface	NOUN
ap-9258	14	29	area	area	NOUN
ap-9258	14	30	or	or	CCONJ
ap-9258	14	31	the	the	DET
ap-9258	14	32	number	number	NOUN
ap-9258	14	33	of	of	ADP
ap-9258	14	34	sides	side	NOUN
ap-9258	14	35	.	.	PUNCT
ap-9258	15	1	the	the	DET
ap-9258	15	2	theoretical	theoretical	ADJ
ap-9258	15	3	results	result	NOUN
ap-9258	15	4	were	be	AUX
ap-9258	15	5	validated	validate	VERB
ap-9258	15	6	using	use	VERB
ap-9258	15	7	the	the	DET
ap-9258	15	8	finite	finite	ADJ
ap-9258	15	9	element	element	NOUN
ap-9258	15	10	method	method	NOUN
ap-9258	15	11	with	with	ADP
ap-9258	15	12	an	an	DET
ap-9258	15	13	excellent	excellent	ADJ
ap-9258	15	14	compliance	compliance	NOUN
ap-9258	15	15	.	.	PUNCT
ap-9258	16	1	keywords	keyword	NOUN
ap-9258	16	2	:	:	PUNCT
ap-9258	16	3	polygonal	polygonal	ADJ
ap-9258	16	4	piston	piston	NOUN
ap-9258	16	5	source	source	NOUN
ap-9258	16	6	,	,	PUNCT
ap-9258	16	7	acoustic	acoustic	ADJ
ap-9258	16	8	transducer	transducer	NOUN
ap-9258	16	9	,	,	PUNCT
ap-9258	16	10	rayleigh	rayleigh	PROPN
ap-9258	16	11	integral	integral	ADJ
ap-9258	16	12	,	,	PUNCT
ap-9258	16	13	radiation	radiation	NOUN
ap-9258	16	14	beam	beam	NOUN
ap-9258	16	15	,	,	PUNCT
ap-9258	16	16	finite	finite	PROPN
ap-9258	16	17	element	element	NOUN
ap-9258	16	18	analysis	analysis	NOUN
ap-9258	16	19	.	.	PUNCT
ap-9258	17	1	1	1	X
ap-9258	17	2	.	.	X
ap-9258	17	3	introduction	introduction	NOUN
ap-9258	17	4	the	the	DET
ap-9258	17	5	acoustic	acoustic	ADJ
ap-9258	17	6	transducer	transducer	NOUN
ap-9258	17	7	technology	technology	NOUN
ap-9258	17	8	is	be	AUX
ap-9258	17	9	relevant	relevant	ADJ
ap-9258	17	10	in	in	ADP
ap-9258	17	11	many	many	ADJ
ap-9258	17	12	areas	area	NOUN
ap-9258	17	13	of	of	ADP
ap-9258	17	14	contemporary	contemporary	ADJ
ap-9258	17	15	applications	application	NOUN
ap-9258	17	16	,	,	PUNCT
ap-9258	17	17	such	such	ADJ
ap-9258	17	18	as	as	ADP
ap-9258	17	19	underwater	underwater	ADJ
ap-9258	17	20	sonar	sonar	NOUN
ap-9258	18	1	[	[	X
ap-9258	18	2	1	1	NUM
ap-9258	18	3	]	]	PUNCT
ap-9258	18	4	,	,	PUNCT
ap-9258	18	5	biomedical	biomedical	ADJ
ap-9258	18	6	diagnosis	diagnosis	NOUN
ap-9258	19	1	[	[	X
ap-9258	19	2	2	2	NUM
ap-9258	19	3	]	]	PUNCT
ap-9258	19	4	,	,	PUNCT
ap-9258	19	5	fluid	fluid	ADJ
ap-9258	19	6	flow	flow	NOUN
ap-9258	19	7	and	and	CCONJ
ap-9258	19	8	heat	heat	NOUN
ap-9258	19	9	transfers	transfer	NOUN
ap-9258	19	10	[	[	X
ap-9258	19	11	3	3	NUM
ap-9258	19	12	]	]	PUNCT
ap-9258	19	13	,	,	PUNCT
ap-9258	19	14	energy	energy	NOUN
ap-9258	19	15	harvesting	harvesting	NOUN
ap-9258	20	1	[	[	X
ap-9258	20	2	4	4	NUM
ap-9258	20	3	]	]	PUNCT
ap-9258	20	4	,	,	PUNCT
ap-9258	20	5	non	non	ADJ
ap-9258	20	6	-	-	ADJ
ap-9258	20	7	destructive	destructive	ADJ
ap-9258	20	8	testing	testing	NOUN
ap-9258	20	9	[	[	X
ap-9258	20	10	5	5	NUM
ap-9258	20	11	]	]	PUNCT
ap-9258	20	12	,	,	PUNCT
ap-9258	20	13	and	and	CCONJ
ap-9258	20	14	enhanced	enhance	VERB
ap-9258	20	15	oil	oil	NOUN
ap-9258	20	16	recovery	recovery	NOUN
ap-9258	21	1	[	[	X
ap-9258	21	2	6	6	NUM
ap-9258	21	3	]	]	PUNCT
ap-9258	21	4	.	.	PUNCT
ap-9258	22	1	in	in	ADP
ap-9258	22	2	underwater	underwater	ADJ
ap-9258	22	3	applications	application	NOUN
ap-9258	22	4	,	,	PUNCT
ap-9258	22	5	acoustic	acoustic	ADJ
ap-9258	22	6	transducers	transducer	NOUN
ap-9258	22	7	are	be	AUX
ap-9258	22	8	used	use	VERB
ap-9258	22	9	as	as	ADP
ap-9258	22	10	sensors	sensor	NOUN
ap-9258	22	11	through	through	ADP
ap-9258	22	12	the	the	DET
ap-9258	22	13	technology	technology	NOUN
ap-9258	22	14	of	of	ADP
ap-9258	22	15	transmission	transmission	NOUN
ap-9258	22	16	of	of	ADP
ap-9258	22	17	sound	sound	ADJ
ap-9258	22	18	waves	wave	NOUN
ap-9258	22	19	for	for	ADP
ap-9258	22	20	the	the	DET
ap-9258	22	21	purpose	purpose	NOUN
ap-9258	22	22	of	of	ADP
ap-9258	22	23	remote	remote	ADJ
ap-9258	22	24	communication	communication	NOUN
ap-9258	22	25	,	,	PUNCT
ap-9258	22	26	imaging	imaging	NOUN
ap-9258	22	27	,	,	PUNCT
ap-9258	22	28	or	or	CCONJ
ap-9258	22	29	detection	detection	NOUN
ap-9258	22	30	[	[	X
ap-9258	22	31	7	7	NUM
ap-9258	22	32	,	,	PUNCT
ap-9258	22	33	8	8	NUM
ap-9258	22	34	]	]	PUNCT
ap-9258	22	35	.	.	PUNCT
ap-9258	23	1	one	one	NUM
ap-9258	23	2	of	of	ADP
ap-9258	23	3	the	the	DET
ap-9258	23	4	output	output	NOUN
ap-9258	23	5	characteristics	characteristic	NOUN
ap-9258	23	6	for	for	ADP
ap-9258	23	7	determining	determine	VERB
ap-9258	23	8	the	the	DET
ap-9258	23	9	performance	performance	NOUN
ap-9258	23	10	of	of	ADP
ap-9258	23	11	such	such	ADJ
ap-9258	23	12	devices	device	NOUN
ap-9258	23	13	is	be	AUX
ap-9258	23	14	a	a	DET
ap-9258	23	15	beam	beam	NOUN
ap-9258	23	16	pattern	pattern	NOUN
ap-9258	23	17	.	.	PUNCT
ap-9258	24	1	the	the	DET
ap-9258	24	2	beam	beam	NOUN
ap-9258	24	3	pattern	pattern	NOUN
ap-9258	24	4	is	be	AUX
ap-9258	24	5	a	a	DET
ap-9258	24	6	logarithmic	logarithmic	ADJ
ap-9258	24	7	function	function	NOUN
ap-9258	24	8	(	(	PUNCT
ap-9258	24	9	decibel	decibel	NOUN
ap-9258	24	10	scale	scale	NOUN
ap-9258	24	11	)	)	PUNCT
ap-9258	24	12	of	of	ADP
ap-9258	24	13	an	an	DET
ap-9258	24	14	angle	angle	NOUN
ap-9258	24	15	-	-	PUNCT
ap-9258	24	16	dependent	dependent	ADJ
ap-9258	24	17	characteristic	characteristic	NOUN
ap-9258	24	18	called	call	VERB
ap-9258	24	19	the	the	DET
ap-9258	24	20	directivity	directivity	NOUN
ap-9258	24	21	factor	factor	NOUN
ap-9258	24	22	.	.	PUNCT
ap-9258	25	1	the	the	DET
ap-9258	25	2	directional	directional	ADJ
ap-9258	25	3	factor	factor	NOUN
ap-9258	25	4	is	be	AUX
ap-9258	25	5	strongly	strongly	ADV
ap-9258	25	6	influenced	influence	VERB
ap-9258	25	7	by	by	ADP
ap-9258	25	8	the	the	DET
ap-9258	25	9	combined	combine	VERB
ap-9258	25	10	effect	effect	NOUN
ap-9258	25	11	of	of	ADP
ap-9258	25	12	the	the	DET
ap-9258	25	13	area	area	NOUN
ap-9258	25	14	of	of	ADP
ap-9258	25	15	its	its	PRON
ap-9258	25	16	radiating	radiate	VERB
ap-9258	25	17	surface	surface	NOUN
ap-9258	25	18	and	and	CCONJ
ap-9258	25	19	the	the	DET
ap-9258	25	20	frequency	frequency	NOUN
ap-9258	25	21	of	of	ADP
ap-9258	25	22	operation	operation	NOUN
ap-9258	25	23	.	.	PUNCT
ap-9258	26	1	this	this	PRON
ap-9258	26	2	makes	make	VERB
ap-9258	26	3	the	the	DET
ap-9258	26	4	geometric	geometric	ADJ
ap-9258	26	5	dimensions	dimension	NOUN
ap-9258	26	6	of	of	ADP
ap-9258	26	7	an	an	DET
ap-9258	26	8	acoustic	acoustic	ADJ
ap-9258	26	9	element	element	NOUN
ap-9258	26	10	a	a	DET
ap-9258	26	11	critical	critical	ADJ
ap-9258	26	12	aspect	aspect	NOUN
ap-9258	26	13	of	of	ADP
ap-9258	26	14	an	an	DET
ap-9258	26	15	effective	effective	ADJ
ap-9258	26	16	design	design	NOUN
ap-9258	26	17	[	[	X
ap-9258	26	18	9	9	NUM
ap-9258	26	19	]	]	PUNCT
ap-9258	26	20	.	.	PUNCT
ap-9258	27	1	in	in	ADP
ap-9258	27	2	addition	addition	NOUN
ap-9258	27	3	,	,	PUNCT
ap-9258	27	4	the	the	DET
ap-9258	27	5	surface	surface	NOUN
ap-9258	27	6	geometry	geometry	NOUN
ap-9258	27	7	of	of	ADP
ap-9258	27	8	individual	individual	ADJ
ap-9258	27	9	component	component	NOUN
ap-9258	27	10	transducer	transducer	NOUN
ap-9258	27	11	elements	element	NOUN
ap-9258	27	12	affects	affect	VERB
ap-9258	27	13	both	both	CCONJ
ap-9258	27	14	the	the	DET
ap-9258	27	15	overall	overall	ADJ
ap-9258	27	16	performance	performance	NOUN
ap-9258	27	17	and	and	CCONJ
ap-9258	27	18	the	the	DET
ap-9258	27	19	optimisation	optimisation	NOUN
ap-9258	27	20	of	of	ADP
ap-9258	27	21	inter	inter	ADJ
ap-9258	27	22	-	-	ADJ
ap-9258	27	23	element	element	ADJ
ap-9258	27	24	spacing	spacing	NOUN
ap-9258	27	25	in	in	ADP
ap-9258	27	26	an	an	DET
ap-9258	27	27	array	array	NOUN
ap-9258	27	28	transducer	transducer	NOUN
ap-9258	27	29	structure	structure	NOUN
ap-9258	27	30	.	.	PUNCT
ap-9258	28	1	for	for	ADP
ap-9258	28	2	the	the	DET
ap-9258	28	3	beam	beam	NOUN
ap-9258	28	4	pattern	pattern	NOUN
ap-9258	28	5	synthesis	synthesis	NOUN
ap-9258	28	6	,	,	PUNCT
ap-9258	28	7	a	a	DET
ap-9258	28	8	single	single	ADJ
ap-9258	28	9	transducer	transducer	NOUN
ap-9258	28	10	is	be	AUX
ap-9258	28	11	considered	consider	VERB
ap-9258	28	12	as	as	ADP
ap-9258	28	13	an	an	DET
ap-9258	28	14	elastic	elastic	ADJ
ap-9258	28	15	membrane	membrane	NOUN
ap-9258	28	16	vibrating	vibrate	VERB
ap-9258	28	17	like	like	ADP
ap-9258	28	18	an	an	DET
ap-9258	28	19	acoustic	acoustic	ADJ
ap-9258	28	20	piston	piston	NOUN
ap-9258	28	21	.	.	PUNCT
ap-9258	29	1	the	the	DET
ap-9258	29	2	directional	directional	ADJ
ap-9258	29	3	factor	factor	NOUN
ap-9258	29	4	of	of	ADP
ap-9258	29	5	a	a	DET
ap-9258	29	6	circular	circular	ADJ
ap-9258	29	7	piston	piston	NOUN
ap-9258	29	8	on	on	ADP
ap-9258	29	9	a	a	DET
ap-9258	29	10	rigid	rigid	ADJ
ap-9258	29	11	infinite	infinite	ADJ
ap-9258	29	12	baffle	baffle	NOUN
ap-9258	29	13	is	be	AUX
ap-9258	29	14	well	well	ADV
ap-9258	29	15	known	know	VERB
ap-9258	29	16	and	and	CCONJ
ap-9258	29	17	has	have	AUX
ap-9258	29	18	been	be	AUX
ap-9258	29	19	used	use	VERB
ap-9258	29	20	in	in	ADP
ap-9258	29	21	several	several	ADJ
ap-9258	29	22	studies	study	NOUN
ap-9258	29	23	[	[	X
ap-9258	29	24	10–16	10–16	NUM
ap-9258	29	25	]	]	PUNCT
ap-9258	29	26	.	.	PUNCT
ap-9258	30	1	however	however	ADV
ap-9258	30	2	,	,	PUNCT
ap-9258	30	3	circular	circular	ADJ
ap-9258	30	4	pistons	piston	NOUN
ap-9258	30	5	are	be	AUX
ap-9258	30	6	unsuitable	unsuitable	ADJ
ap-9258	30	7	for	for	ADP
ap-9258	30	8	composing	compose	VERB
ap-9258	30	9	an	an	DET
ap-9258	30	10	array	array	NOUN
ap-9258	30	11	transducer	transducer	NOUN
ap-9258	30	12	of	of	ADP
ap-9258	30	13	densely	densely	ADV
ap-9258	30	14	packed	pack	VERB
ap-9258	30	15	elements	element	NOUN
ap-9258	30	16	.	.	PUNCT
ap-9258	31	1	they	they	PRON
ap-9258	31	2	typically	typically	ADV
ap-9258	31	3	leave	leave	VERB
ap-9258	31	4	inevitable	inevitable	ADJ
ap-9258	31	5	gaps	gap	NOUN
ap-9258	31	6	between	between	ADP
ap-9258	31	7	their	their	PRON
ap-9258	31	8	edges	edge	NOUN
ap-9258	31	9	contributing	contribute	VERB
ap-9258	31	10	to	to	ADP
ap-9258	31	11	poor	poor	ADJ
ap-9258	31	12	space	space	NOUN
ap-9258	31	13	conservation	conservation	NOUN
ap-9258	31	14	[	[	X
ap-9258	31	15	17	17	NUM
ap-9258	31	16	,	,	PUNCT
ap-9258	31	17	18	18	NUM
ap-9258	31	18	]	]	PUNCT
ap-9258	31	19	and	and	CCONJ
ap-9258	31	20	a	a	DET
ap-9258	31	21	considerable	considerable	ADJ
ap-9258	31	22	loss	loss	NOUN
ap-9258	31	23	in	in	ADP
ap-9258	31	24	the	the	DET
ap-9258	31	25	radiated	radiate	VERB
ap-9258	31	26	power	power	NOUN
ap-9258	31	27	[	[	X
ap-9258	31	28	19	19	NUM
ap-9258	31	29	]	]	PUNCT
ap-9258	31	30	.	.	PUNCT
ap-9258	32	1	meanwhile	meanwhile	ADV
ap-9258	32	2	,	,	PUNCT
ap-9258	32	3	acoustic	acoustic	ADJ
ap-9258	32	4	pistons	piston	NOUN
ap-9258	32	5	with	with	ADP
ap-9258	32	6	flat	flat	ADJ
ap-9258	32	7	surfaces	surface	NOUN
ap-9258	32	8	such	such	ADJ
ap-9258	32	9	as	as	ADP
ap-9258	32	10	polygons	polygon	NOUN
ap-9258	32	11	have	have	VERB
ap-9258	32	12	more	more	ADJ
ap-9258	32	13	prospects	prospect	NOUN
ap-9258	32	14	in	in	ADP
ap-9258	32	15	providing	provide	VERB
ap-9258	32	16	a	a	DET
ap-9258	32	17	more	more	ADV
ap-9258	32	18	compact	compact	ADJ
ap-9258	32	19	transducer	transducer	NOUN
ap-9258	32	20	structure	structure	NOUN
ap-9258	32	21	[	[	X
ap-9258	32	22	20	20	NUM
ap-9258	32	23	]	]	PUNCT
ap-9258	32	24	.	.	PUNCT
ap-9258	33	1	in	in	ADP
ap-9258	33	2	addition	addition	NOUN
ap-9258	33	3	,	,	PUNCT
ap-9258	33	4	their	their	PRON
ap-9258	33	5	side	side	NOUN
ap-9258	33	6	lengths	length	NOUN
ap-9258	33	7	can	can	AUX
ap-9258	33	8	be	be	AUX
ap-9258	33	9	varied	varied	ADJ
ap-9258	33	10	independently	independently	ADV
ap-9258	33	11	to	to	PART
ap-9258	33	12	increase	increase	VERB
ap-9258	33	13	the	the	DET
ap-9258	33	14	radiating	radiate	VERB
ap-9258	33	15	surface	surface	NOUN
ap-9258	33	16	area	area	NOUN
ap-9258	33	17	without	without	ADP
ap-9258	33	18	increasing	increase	VERB
ap-9258	33	19	the	the	DET
ap-9258	33	20	size	size	NOUN
ap-9258	33	21	in	in	ADP
ap-9258	33	22	all	all	DET
ap-9258	33	23	the	the	DET
ap-9258	33	24	directions	direction	NOUN
ap-9258	33	25	.	.	PUNCT
ap-9258	34	1	this	this	PRON
ap-9258	34	2	offers	offer	VERB
ap-9258	34	3	a	a	DET
ap-9258	34	4	more	more	ADV
ap-9258	34	5	efficient	efficient	ADJ
ap-9258	34	6	way	way	NOUN
ap-9258	34	7	to	to	PART
ap-9258	34	8	control	control	VERB
ap-9258	34	9	the	the	DET
ap-9258	34	10	overall	overall	ADJ
ap-9258	34	11	size	size	NOUN
ap-9258	34	12	of	of	ADP
ap-9258	34	13	the	the	DET
ap-9258	34	14	transducer	transducer	NOUN
ap-9258	34	15	than	than	ADP
ap-9258	34	16	using	use	VERB
ap-9258	34	17	the	the	DET
ap-9258	34	18	circular	circular	ADJ
ap-9258	34	19	pistons	piston	NOUN
ap-9258	34	20	without	without	ADP
ap-9258	34	21	the	the	DET
ap-9258	34	22	liability	liability	NOUN
ap-9258	34	23	of	of	ADP
ap-9258	34	24	an	an	DET
ap-9258	34	25	added	add	VERB
ap-9258	34	26	cost	cost	NOUN
ap-9258	34	27	[	[	X
ap-9258	34	28	21	21	NUM
ap-9258	34	29	]	]	PUNCT
ap-9258	34	30	.	.	PUNCT
ap-9258	35	1	while	while	SCONJ
ap-9258	35	2	the	the	DET
ap-9258	35	3	square	square	ADJ
ap-9258	35	4	and	and	CCONJ
ap-9258	35	5	rectangular	rectangular	ADJ
ap-9258	35	6	pistons	piston	NOUN
ap-9258	35	7	are	be	AUX
ap-9258	35	8	also	also	ADV
ap-9258	35	9	being	be	AUX
ap-9258	35	10	fairly	fairly	ADV
ap-9258	35	11	used	use	VERB
ap-9258	35	12	in	in	ADP
ap-9258	35	13	few	few	ADJ
ap-9258	35	14	instances	instance	NOUN
ap-9258	35	15	[	[	X
ap-9258	35	16	22	22	NUM
ap-9258	35	17	,	,	PUNCT
ap-9258	35	18	23	23	NUM
ap-9258	35	19	]	]	PUNCT
ap-9258	35	20	,	,	PUNCT
ap-9258	35	21	the	the	DET
ap-9258	35	22	higher	higher	ADV
ap-9258	35	23	-	-	PUNCT
ap-9258	35	24	sided	sided	ADJ
ap-9258	35	25	polygons	polygon	NOUN
ap-9258	35	26	such	such	ADJ
ap-9258	35	27	as	as	ADP
ap-9258	35	28	the	the	DET
ap-9258	35	29	hexagon	hexagon	NOUN
ap-9258	35	30	have	have	VERB
ap-9258	35	31	more	more	ADJ
ap-9258	35	32	elements	element	NOUN
ap-9258	35	33	in	in	ADP
ap-9258	35	34	their	their	PRON
ap-9258	35	35	primary	primary	ADJ
ap-9258	35	36	neighbourhood	neighbourhood	NOUN
ap-9258	35	37	,	,	PUNCT
ap-9258	35	38	which	which	PRON
ap-9258	35	39	enhances	enhance	VERB
ap-9258	35	40	their	their	PRON
ap-9258	35	41	radiation	radiation	NOUN
ap-9258	35	42	characteristics	characteristic	NOUN
ap-9258	35	43	in	in	ADP
ap-9258	35	44	a	a	DET
ap-9258	35	45	staggered	staggered	ADJ
ap-9258	35	46	array	array	NOUN
ap-9258	35	47	configuration	configuration	NOUN
ap-9258	36	1	[	[	X
ap-9258	36	2	20	20	NUM
ap-9258	36	3	]	]	PUNCT
ap-9258	36	4	.	.	PUNCT
ap-9258	37	1	470	470	NUM
ap-9258	37	2	https://doi.org/10.14311/ap.2024.64.0470	https://doi.org/10.14311/ap.2024.64.0470	PROPN
ap-9258	37	3	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-9258	37	4	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-9258	37	5	vol	vol	NOUN
ap-9258	37	6	.	.	PROPN
ap-9258	37	7	64	64	NUM
ap-9258	37	8	no	no	NOUN
ap-9258	37	9	.	.	PUNCT
ap-9258	38	1	5/2024	5/2024	ADJ
ap-9258	38	2	acoustic	acoustic	ADJ
ap-9258	38	3	radiation	radiation	NOUN
ap-9258	38	4	beam	beam	NOUN
ap-9258	38	5	patterns	pattern	NOUN
ap-9258	38	6	of	of	ADP
ap-9258	38	7	different	different	ADJ
ap-9258	38	8	polygonal	polygonal	NOUN
ap-9258	38	9	.	.	PUNCT
ap-9258	38	10	.	.	PUNCT
ap-9258	38	11	.	.	PUNCT
ap-9258	39	1	to	to	ADP
ap-9258	39	2	date	date	NOUN
ap-9258	39	3	,	,	PUNCT
ap-9258	39	4	there	there	PRON
ap-9258	39	5	has	have	AUX
ap-9258	39	6	been	be	AUX
ap-9258	39	7	no	no	DET
ap-9258	39	8	independent	independent	ADJ
ap-9258	39	9	study	study	NOUN
ap-9258	39	10	that	that	PRON
ap-9258	39	11	has	have	AUX
ap-9258	39	12	exclusively	exclusively	ADV
ap-9258	39	13	analysed	analyse	VERB
ap-9258	39	14	these	these	DET
ap-9258	39	15	polygonal	polygonal	ADJ
ap-9258	39	16	surfaces	surface	NOUN
ap-9258	39	17	and	and	CCONJ
ap-9258	39	18	effectively	effectively	ADV
ap-9258	39	19	characterised	characterise	VERB
ap-9258	39	20	their	their	PRON
ap-9258	39	21	acoustic	acoustic	ADJ
ap-9258	39	22	radiation	radiation	NOUN
ap-9258	39	23	performance	performance	NOUN
ap-9258	39	24	.	.	PUNCT
ap-9258	40	1	roh	roh	PROPN
ap-9258	40	2	et	et	PROPN
ap-9258	40	3	al	al	PROPN
ap-9258	40	4	.	.	PROPN
ap-9258	40	5	made	make	VERB
ap-9258	40	6	an	an	DET
ap-9258	40	7	effort	effort	NOUN
ap-9258	40	8	in	in	ADP
ap-9258	40	9	that	that	DET
ap-9258	40	10	direction	direction	NOUN
ap-9258	40	11	but	but	CCONJ
ap-9258	40	12	apparently	apparently	ADV
ap-9258	40	13	made	make	VERB
ap-9258	40	14	no	no	DET
ap-9258	40	15	distinction	distinction	NOUN
ap-9258	40	16	between	between	ADP
ap-9258	40	17	the	the	DET
ap-9258	40	18	rectangular	rectangular	ADJ
ap-9258	40	19	and	and	CCONJ
ap-9258	40	20	square	square	ADJ
ap-9258	40	21	sources	source	NOUN
ap-9258	40	22	while	while	SCONJ
ap-9258	40	23	some	some	DET
ap-9258	40	24	weird	weird	ADJ
ap-9258	40	25	non	non	ADJ
ap-9258	40	26	-	-	ADJ
ap-9258	40	27	symmetrical	symmetrical	ADJ
ap-9258	40	28	geometries	geometry	NOUN
ap-9258	40	29	,	,	PUNCT
ap-9258	40	30	such	such	ADJ
ap-9258	40	31	as	as	ADP
ap-9258	40	32	the	the	DET
ap-9258	40	33	triangle	triangle	NOUN
ap-9258	40	34	and	and	CCONJ
ap-9258	40	35	pentagon	pentagon	PROPN
ap-9258	40	36	,	,	PUNCT
ap-9258	40	37	were	be	AUX
ap-9258	40	38	not	not	PART
ap-9258	40	39	included	include	VERB
ap-9258	40	40	[	[	X
ap-9258	40	41	19	19	NUM
ap-9258	40	42	]	]	PUNCT
ap-9258	40	43	.	.	PUNCT
ap-9258	41	1	consequently	consequently	ADV
ap-9258	41	2	,	,	PUNCT
ap-9258	41	3	this	this	DET
ap-9258	41	4	study	study	NOUN
ap-9258	41	5	took	take	VERB
ap-9258	41	6	a	a	DET
ap-9258	41	7	more	more	ADV
ap-9258	41	8	comprehensive	comprehensive	ADJ
ap-9258	41	9	approach	approach	NOUN
ap-9258	41	10	on	on	ADP
ap-9258	41	11	this	this	DET
ap-9258	41	12	subject	subject	NOUN
ap-9258	41	13	.	.	PUNCT
ap-9258	42	1	the	the	DET
ap-9258	42	2	directional	directional	ADJ
ap-9258	42	3	factors	factor	NOUN
ap-9258	42	4	of	of	ADP
ap-9258	42	5	nine	nine	NUM
ap-9258	42	6	(	(	PUNCT
ap-9258	42	7	9	9	NUM
ap-9258	42	8	)	)	PUNCT
ap-9258	42	9	acoustic	acoustic	ADJ
ap-9258	42	10	pistons	piston	NOUN
ap-9258	42	11	sources	source	NOUN
ap-9258	42	12	having	have	VERB
ap-9258	42	13	3–10	3–10	PROPN
ap-9258	42	14	sided	sided	ADJ
ap-9258	42	15	polygon	polygon	NOUN
ap-9258	42	16	surfaces	surface	NOUN
ap-9258	42	17	were	be	AUX
ap-9258	42	18	characterised	characterise	VERB
ap-9258	42	19	and	and	CCONJ
ap-9258	42	20	compared	compare	VERB
ap-9258	42	21	with	with	ADP
ap-9258	42	22	that	that	PRON
ap-9258	42	23	of	of	ADP
ap-9258	42	24	the	the	DET
ap-9258	42	25	circular	circular	ADJ
ap-9258	42	26	piston	piston	NOUN
ap-9258	42	27	on	on	ADP
ap-9258	42	28	a	a	DET
ap-9258	42	29	rigid	rigid	ADJ
ap-9258	42	30	baffle	baffle	NOUN
ap-9258	42	31	,	,	PUNCT
ap-9258	42	32	which	which	PRON
ap-9258	42	33	was	be	AUX
ap-9258	42	34	used	use	VERB
ap-9258	42	35	as	as	ADP
ap-9258	42	36	the	the	DET
ap-9258	42	37	standard	standard	NOUN
ap-9258	42	38	.	.	PUNCT
ap-9258	43	1	using	use	VERB
ap-9258	43	2	the	the	DET
ap-9258	43	3	finite	finite	ADJ
ap-9258	43	4	element	element	NOUN
ap-9258	43	5	commercial	commercial	ADJ
ap-9258	43	6	software	software	NOUN
ap-9258	43	7	,	,	PUNCT
ap-9258	43	8	pzflex	pzflex	ADJ
ap-9258	43	9	®	®	NOUN
ap-9258	43	10	,	,	PUNCT
ap-9258	43	11	tonpilz	tonpilz	NOUN
ap-9258	43	12	transducer	transducer	NOUN
ap-9258	43	13	structures	structure	NOUN
ap-9258	43	14	were	be	AUX
ap-9258	43	15	modelled	model	VERB
ap-9258	43	16	and	and	CCONJ
ap-9258	43	17	simulated	simulate	VERB
ap-9258	43	18	using	use	VERB
ap-9258	43	19	the	the	DET
ap-9258	43	20	geometries	geometry	NOUN
ap-9258	43	21	of	of	ADP
ap-9258	43	22	the	the	DET
ap-9258	43	23	piston	piston	NOUN
ap-9258	43	24	sources	source	NOUN
ap-9258	43	25	for	for	ADP
ap-9258	43	26	the	the	DET
ap-9258	43	27	shapes	shape	NOUN
ap-9258	43	28	of	of	ADP
ap-9258	43	29	the	the	DET
ap-9258	43	30	head	head	NOUN
ap-9258	43	31	masses	mass	VERB
ap-9258	43	32	to	to	PART
ap-9258	43	33	validate	validate	VERB
ap-9258	43	34	the	the	DET
ap-9258	43	35	theoretical	theoretical	ADJ
ap-9258	43	36	results	result	NOUN
ap-9258	43	37	.	.	PUNCT
ap-9258	44	1	the	the	DET
ap-9258	44	2	comparison	comparison	NOUN
ap-9258	44	3	between	between	ADP
ap-9258	44	4	the	the	DET
ap-9258	44	5	theoretical	theoretical	ADJ
ap-9258	44	6	and	and	CCONJ
ap-9258	44	7	fem	fem	NOUN
ap-9258	44	8	beam	beam	NOUN
ap-9258	44	9	patterns	pattern	NOUN
ap-9258	44	10	showed	show	VERB
ap-9258	44	11	good	good	ADJ
ap-9258	44	12	agreements	agreement	NOUN
ap-9258	44	13	.	.	PUNCT
ap-9258	45	1	finally	finally	ADV
ap-9258	45	2	,	,	PUNCT
ap-9258	45	3	the	the	DET
ap-9258	45	4	expression	expression	NOUN
ap-9258	45	5	for	for	ADP
ap-9258	45	6	the	the	DET
ap-9258	45	7	directional	directional	ADJ
ap-9258	45	8	factors	factor	NOUN
ap-9258	45	9	were	be	AUX
ap-9258	45	10	standardised	standardise	VERB
ap-9258	45	11	to	to	PART
ap-9258	45	12	facilitate	facilitate	VERB
ap-9258	45	13	their	their	PRON
ap-9258	45	14	adoption	adoption	NOUN
ap-9258	45	15	in	in	ADP
ap-9258	45	16	subsequent	subsequent	ADJ
ap-9258	45	17	designs	design	NOUN
ap-9258	45	18	.	.	PUNCT
ap-9258	46	1	2	2	X
ap-9258	46	2	.	.	X
ap-9258	46	3	equivalent	equivalent	ADJ
ap-9258	46	4	surface	surface	NOUN
ap-9258	46	5	area	area	NOUN
ap-9258	46	6	of	of	ADP
ap-9258	46	7	the	the	DET
ap-9258	46	8	piston	piston	NOUN
ap-9258	46	9	sources	source	NOUN
ap-9258	46	10	the	the	DET
ap-9258	46	11	circular	circular	ADJ
ap-9258	46	12	piston	piston	NOUN
ap-9258	46	13	of	of	ADP
ap-9258	46	14	a	a	DET
ap-9258	46	15	given	give	VERB
ap-9258	46	16	radius	radius	NOUN
ap-9258	46	17	ac	ac	PROPN
ap-9258	46	18	is	be	AUX
ap-9258	46	19	used	use	VERB
ap-9258	46	20	as	as	ADP
ap-9258	46	21	the	the	DET
ap-9258	46	22	standard	standard	ADJ
ap-9258	46	23	reference	reference	NOUN
ap-9258	46	24	as	as	SCONJ
ap-9258	46	25	shown	show	VERB
ap-9258	46	26	in	in	ADP
ap-9258	46	27	figure	figure	NOUN
ap-9258	46	28	1	1	NUM
ap-9258	46	29	.	.	PUNCT
ap-9258	46	30	figure	figure	NOUN
ap-9258	46	31	2	2	NUM
ap-9258	46	32	shows	show	VERB
ap-9258	46	33	the	the	DET
ap-9258	46	34	polygonal	polygonal	ADJ
ap-9258	46	35	pistons	piston	NOUN
ap-9258	46	36	with	with	ADP
ap-9258	46	37	three	three	NUM
ap-9258	46	38	to	to	PART
ap-9258	46	39	ten	ten	NUM
ap-9258	46	40	surfaces	surface	NOUN
ap-9258	46	41	proposed	propose	VERB
ap-9258	46	42	for	for	ADP
ap-9258	46	43	this	this	DET
ap-9258	46	44	study	study	NOUN
ap-9258	46	45	,	,	PUNCT
ap-9258	46	46	respectively	respectively	ADV
ap-9258	46	47	.	.	PUNCT
ap-9258	47	1	the	the	DET
ap-9258	47	2	half	half	ADJ
ap-9258	47	3	-	-	PUNCT
ap-9258	47	4	side	side	NOUN
ap-9258	47	5	length	length	NOUN
ap-9258	47	6	(	(	PUNCT
ap-9258	47	7	hsl	hsl	NOUN
ap-9258	47	8	)	)	PUNCT
ap-9258	47	9	a	a	PRON
ap-9258	47	10	of	of	ADP
ap-9258	47	11	each	each	PRON
ap-9258	47	12	of	of	ADP
ap-9258	47	13	them	they	PRON
ap-9258	47	14	carries	carry	VERB
ap-9258	47	15	the	the	DET
ap-9258	47	16	subscripts	subscript	NOUN
ap-9258	47	17	denoting	denote	VERB
ap-9258	47	18	the	the	DET
ap-9258	47	19	first	first	ADJ
ap-9258	47	20	letter	letter	NOUN
ap-9258	47	21	of	of	ADP
ap-9258	47	22	their	their	PRON
ap-9258	47	23	respective	respective	ADJ
ap-9258	47	24	names	name	NOUN
ap-9258	47	25	except	except	SCONJ
ap-9258	47	26	for	for	ADP
ap-9258	47	27	the	the	DET
ap-9258	47	28	hexagon	hexagon	NOUN
ap-9258	47	29	defined	define	VERB
ap-9258	47	30	as	as	ADP
ap-9258	47	31	ax	ax	NOUN
ap-9258	47	32	in	in	ADP
ap-9258	47	33	figure	figure	NOUN
ap-9258	47	34	2e	2e	NUM
ap-9258	47	35	.	.	PUNCT
ap-9258	48	1	all	all	DET
ap-9258	48	2	the	the	DET
ap-9258	48	3	polygons	polygon	NOUN
ap-9258	48	4	are	be	AUX
ap-9258	48	5	regular	regular	ADJ
ap-9258	48	6	except	except	SCONJ
ap-9258	48	7	the	the	DET
ap-9258	48	8	rectangle	rectangle	NOUN
ap-9258	48	9	where	where	SCONJ
ap-9258	48	10	one	one	NUM
ap-9258	48	11	side	side	NOUN
ap-9258	48	12	is	be	AUX
ap-9258	48	13	equal	equal	ADJ
ap-9258	48	14	to	to	ADP
ap-9258	48	15	the	the	DET
ap-9258	48	16	diameter	diameter	NOUN
ap-9258	48	17	of	of	ADP
ap-9258	48	18	the	the	DET
ap-9258	48	19	circular	circular	ADJ
ap-9258	48	20	piston	piston	NOUN
ap-9258	48	21	as	as	SCONJ
ap-9258	48	22	shown	show	VERB
ap-9258	48	23	in	in	ADP
ap-9258	48	24	figure	figure	NOUN
ap-9258	48	25	2b	2b	NOUN
ap-9258	48	26	.	.	PUNCT
ap-9258	49	1	the	the	DET
ap-9258	49	2	diameter	diameter	NOUN
ap-9258	49	3	of	of	ADP
ap-9258	49	4	the	the	DET
ap-9258	49	5	circular	circular	ADJ
ap-9258	49	6	surface	surface	NOUN
ap-9258	49	7	is	be	AUX
ap-9258	49	8	specified	specify	VERB
ap-9258	49	9	in	in	ADP
ap-9258	49	10	terms	term	NOUN
ap-9258	49	11	of	of	ADP
ap-9258	49	12	the	the	DET
ap-9258	49	13	wavelength	wavelength	NOUN
ap-9258	49	14	λ	λ	PROPN
ap-9258	49	15	that	that	PRON
ap-9258	49	16	was	be	AUX
ap-9258	49	17	calculated	calculate	VERB
ap-9258	49	18	using	use	VERB
ap-9258	49	19	λ	λ	PROPN
ap-9258	49	20	=	=	PUNCT
ap-9258	49	21	c	c	PROPN
ap-9258	49	22	f	f	PROPN
ap-9258	49	23	,	,	PUNCT
ap-9258	49	24	where	where	SCONJ
ap-9258	49	25	c	c	NOUN
ap-9258	49	26	=	=	SYM
ap-9258	49	27	1	1	NUM
ap-9258	49	28	500	500	NUM
ap-9258	49	29	m	m	VERB
ap-9258	49	30	s−1	s−1	PROPN
ap-9258	49	31	is	be	AUX
ap-9258	49	32	the	the	DET
ap-9258	49	33	acoustic	acoustic	ADJ
ap-9258	49	34	speed	speed	NOUN
ap-9258	49	35	in	in	ADP
ap-9258	49	36	water	water	NOUN
ap-9258	49	37	and	and	CCONJ
ap-9258	49	38	f	f	PROPN
ap-9258	49	39	,	,	PUNCT
ap-9258	49	40	is	be	AUX
ap-9258	49	41	the	the	DET
ap-9258	49	42	given	give	VERB
ap-9258	49	43	frequency	frequency	NOUN
ap-9258	49	44	of	of	ADP
ap-9258	49	45	vibration	vibration	NOUN
ap-9258	49	46	.	.	PUNCT
ap-9258	50	1	it	it	PRON
ap-9258	50	2	is	be	AUX
ap-9258	50	3	instructive	instructive	ADJ
ap-9258	50	4	that	that	SCONJ
ap-9258	50	5	the	the	DET
ap-9258	50	6	radiating	radiate	VERB
ap-9258	50	7	surface	surface	NOUN
ap-9258	50	8	areas	area	NOUN
ap-9258	50	9	must	must	AUX
ap-9258	50	10	be	be	AUX
ap-9258	50	11	the	the	DET
ap-9258	50	12	same	same	ADJ
ap-9258	50	13	for	for	SCONJ
ap-9258	50	14	all	all	DET
ap-9258	50	15	the	the	DET
ap-9258	50	16	piston	piston	NOUN
ap-9258	50	17	sources	source	NOUN
ap-9258	50	18	to	to	PART
ap-9258	50	19	make	make	VERB
ap-9258	50	20	a	a	DET
ap-9258	50	21	realistic	realistic	ADJ
ap-9258	50	22	comparison	comparison	NOUN
ap-9258	50	23	of	of	ADP
ap-9258	50	24	their	their	PRON
ap-9258	50	25	acoustic	acoustic	ADJ
ap-9258	50	26	beam	beam	NOUN
ap-9258	50	27	characteristics	characteristic	NOUN
ap-9258	50	28	.	.	PUNCT
ap-9258	51	1	consequently	consequently	ADV
ap-9258	51	2	,	,	PUNCT
ap-9258	51	3	the	the	DET
ap-9258	51	4	hsl	hsl	NOUN
ap-9258	51	5	of	of	ADP
ap-9258	51	6	all	all	DET
ap-9258	51	7	polygon	polygon	NOUN
ap-9258	51	8	surfaces	surface	NOUN
ap-9258	51	9	are	be	AUX
ap-9258	51	10	determined	determine	VERB
ap-9258	51	11	at	at	ADP
ap-9258	51	12	the	the	DET
ap-9258	51	13	equivalent	equivalent	ADJ
ap-9258	51	14	surface	surface	NOUN
ap-9258	51	15	area	area	NOUN
ap-9258	51	16	of	of	ADP
ap-9258	51	17	the	the	DET
ap-9258	51	18	circular	circular	ADJ
ap-9258	51	19	piston	piston	NOUN
ap-9258	51	20	and	and	CCONJ
ap-9258	51	21	expressed	express	VERB
ap-9258	51	22	in	in	ADP
ap-9258	51	23	terms	term	NOUN
ap-9258	51	24	of	of	ADP
ap-9258	51	25	ac	ac	PROPN
ap-9258	51	26	as	as	SCONJ
ap-9258	51	27	shown	show	VERB
ap-9258	51	28	for	for	ADP
ap-9258	51	29	the	the	DET
ap-9258	51	30	triangle	triangle	NOUN
ap-9258	51	31	in	in	ADP
ap-9258	51	32	equation	equation	NOUN
ap-9258	51	33	(	(	PUNCT
ap-9258	51	34	1	1	NUM
ap-9258	51	35	)	)	PUNCT
ap-9258	51	36	.	.	PUNCT
ap-9258	52	1	from	from	ADP
ap-9258	52	2	this	this	DET
ap-9258	52	3	equation	equation	NOUN
ap-9258	52	4	,	,	PUNCT
ap-9258	52	5	the	the	DET
ap-9258	52	6	hsl	hsl	NOUN
ap-9258	52	7	of	of	ADP
ap-9258	52	8	the	the	DET
ap-9258	52	9	triangle	triangle	NOUN
ap-9258	52	10	at	at	ADP
ap-9258	52	11	is	be	AUX
ap-9258	52	12	determined	determine	VERB
ap-9258	52	13	as	as	ADP
ap-9258	52	14	given	give	VERB
ap-9258	52	15	in	in	ADP
ap-9258	52	16	equation	equation	NOUN
ap-9258	52	17	(	(	PUNCT
ap-9258	52	18	2	2	NUM
ap-9258	52	19	)	)	PUNCT
ap-9258	52	20	.	.	PUNCT
ap-9258	53	1	similarly	similarly	ADV
ap-9258	53	2	,	,	PUNCT
ap-9258	53	3	the	the	DET
ap-9258	53	4	hsl	hsl	NOUN
ap-9258	53	5	for	for	ADP
ap-9258	53	6	the	the	DET
ap-9258	53	7	rectangle	rectangle	NOUN
ap-9258	53	8	and	and	CCONJ
ap-9258	53	9	the	the	DET
ap-9258	53	10	square	square	NOUN
ap-9258	53	11	are	be	AUX
ap-9258	53	12	derived	derive	VERB
ap-9258	53	13	from	from	ADP
ap-9258	53	14	the	the	DET
ap-9258	53	15	equivalent	equivalent	ADJ
ap-9258	53	16	circular	circular	ADJ
ap-9258	53	17	surface	surface	NOUN
ap-9258	53	18	area	area	NOUN
ap-9258	53	19	as	as	SCONJ
ap-9258	53	20	given	give	VERB
ap-9258	53	21	in	in	ADP
ap-9258	53	22	equations	equation	NOUN
ap-9258	53	23	(	(	PUNCT
ap-9258	53	24	3	3	NUM
ap-9258	53	25	)	)	PUNCT
ap-9258	53	26	and	and	CCONJ
ap-9258	53	27	(	(	PUNCT
ap-9258	53	28	4	4	NUM
ap-9258	53	29	)	)	PUNCT
ap-9258	53	30	,	,	PUNCT
ap-9258	53	31	respectively	respectively	ADV
ap-9258	53	32	.	.	PUNCT
ap-9258	54	1	1	1	NUM
ap-9258	54	2	2	2	NUM
ap-9258	54	3	×	×	NOUN
ap-9258	54	4	2at	2at	ADJ
ap-9258	54	5	×	×	NOUN
ap-9258	54	6	at	at	ADP
ap-9258	54	7	tan	tan	PROPN
ap-9258	54	8	60	60	NUM
ap-9258	54	9	=	=	NOUN
ap-9258	54	10	πac	πac	ADP
ap-9258	54	11	2	2	NUM
ap-9258	54	12	,	,	PUNCT
ap-9258	54	13	(	(	PUNCT
ap-9258	54	14	1	1	X
ap-9258	54	15	)	)	PUNCT
ap-9258	54	16	at	at	ADP
ap-9258	54	17	=	=	PUNCT
ap-9258	54	18	(	(	PUNCT
ap-9258	54	19	√	√	PROPN
ap-9258	54	20	π	π	PROPN
ap-9258	54	21	tan	tan	PROPN
ap-9258	54	22	π	π	PROPN
ap-9258	54	23	6	6	NUM
ap-9258	54	24	)	)	PUNCT
ap-9258	54	25	ac	ac	PROPN
ap-9258	54	26	=	=	PUNCT
ap-9258	54	27	(	(	PUNCT
ap-9258	54	28	4	4	NUM
ap-9258	54	29	√	√	NUM
ap-9258	54	30	π2	π2	PROPN
ap-9258	54	31	3	3	NUM
ap-9258	54	32	)	)	PUNCT
ap-9258	54	33	ac	ac	PROPN
ap-9258	54	34	,	,	PUNCT
ap-9258	54	35	(	(	PUNCT
ap-9258	54	36	2	2	X
ap-9258	54	37	)	)	PUNCT
ap-9258	54	38	ar	ar	NOUN
ap-9258	55	1	=	=	SYM
ap-9258	55	2	π	π	PROPN
ap-9258	55	3	4	4	NUM
ap-9258	55	4	ac	ac	PROPN
ap-9258	55	5	,	,	PUNCT
ap-9258	55	6	(	(	PUNCT
ap-9258	55	7	3	3	X
ap-9258	55	8	)	)	PUNCT
ap-9258	55	9	as	as	ADP
ap-9258	55	10	=	=	NOUN
ap-9258	55	11	√	√	PROPN
ap-9258	55	12	π	π	PROPN
ap-9258	55	13	2	2	NUM
ap-9258	55	14	ac	ac	NOUN
ap-9258	55	15	.	.	PUNCT
ap-9258	56	1	(	(	PUNCT
ap-9258	56	2	4	4	NUM
ap-9258	56	3	)	)	PUNCT
ap-9258	56	4	for	for	ADP
ap-9258	56	5	the	the	DET
ap-9258	56	6	high	high	ADJ
ap-9258	56	7	-	-	PUNCT
ap-9258	56	8	sided	sided	ADJ
ap-9258	56	9	polygons	polygon	NOUN
ap-9258	56	10	such	such	ADJ
ap-9258	56	11	as	as	ADP
ap-9258	56	12	the	the	DET
ap-9258	56	13	pentagon	pentagon	PROPN
ap-9258	56	14	shown	show	VERB
ap-9258	56	15	in	in	ADP
ap-9258	56	16	figure	figure	NOUN
ap-9258	56	17	3	3	NUM
ap-9258	56	18	,	,	PUNCT
ap-9258	56	19	the	the	DET
ap-9258	56	20	equivalent	equivalent	ADJ
ap-9258	56	21	area	area	NOUN
ap-9258	56	22	is	be	AUX
ap-9258	56	23	expressed	express	VERB
ap-9258	56	24	in	in	ADP
ap-9258	56	25	equation	equation	NOUN
ap-9258	56	26	(	(	PUNCT
ap-9258	56	27	5	5	NUM
ap-9258	56	28	)	)	PUNCT
ap-9258	56	29	and	and	CCONJ
ap-9258	56	30	the	the	DET
ap-9258	56	31	hsl	hsl	NOUN
ap-9258	56	32	,	,	PUNCT
ap-9258	56	33	ap	ap	PROPN
ap-9258	56	34	is	be	AUX
ap-9258	56	35	determined	determine	VERB
ap-9258	56	36	as	as	ADP
ap-9258	56	37	given	give	VERB
ap-9258	56	38	in	in	ADP
ap-9258	56	39	equation	equation	NOUN
ap-9258	56	40	(	(	PUNCT
ap-9258	56	41	6	6	NUM
ap-9258	56	42	)	)	PUNCT
ap-9258	56	43	.	.	PUNCT
ap-9258	57	1	following	follow	VERB
ap-9258	57	2	the	the	DET
ap-9258	57	3	same	same	ADJ
ap-9258	57	4	approach	approach	NOUN
ap-9258	57	5	for	for	ADP
ap-9258	57	6	other	other	ADJ
ap-9258	57	7	polygons	polygon	NOUN
ap-9258	57	8	,	,	PUNCT
ap-9258	57	9	it	it	PRON
ap-9258	57	10	can	can	AUX
ap-9258	57	11	be	be	AUX
ap-9258	57	12	found	find	VERB
ap-9258	57	13	that	that	SCONJ
ap-9258	57	14	the	the	DET
ap-9258	57	15	hsl	hsl	NOUN
ap-9258	57	16	takes	take	VERB
ap-9258	57	17	the	the	DET
ap-9258	57	18	general	general	ADJ
ap-9258	57	19	form	form	NOUN
ap-9258	57	20	of	of	ADP
ap-9258	57	21	equation	equation	NOUN
ap-9258	57	22	(	(	PUNCT
ap-9258	57	23	7	7	NUM
ap-9258	57	24	)	)	PUNCT
ap-9258	57	25	,	,	PUNCT
ap-9258	57	26	which	which	PRON
ap-9258	57	27	is	be	AUX
ap-9258	57	28	true	true	ADJ
ap-9258	57	29	for	for	ADP
ap-9258	57	30	all	all	DET
ap-9258	57	31	the	the	DET
ap-9258	57	32	polygons	polygon	NOUN
ap-9258	57	33	where	where	SCONJ
ap-9258	57	34	n	n	X
ap-9258	57	35	is	be	AUX
ap-9258	57	36	the	the	DET
ap-9258	57	37	number	number	NOUN
ap-9258	57	38	of	of	ADP
ap-9258	57	39	sides	side	NOUN
ap-9258	57	40	except	except	SCONJ
ap-9258	57	41	the	the	DET
ap-9258	57	42	rectangle	rectangle	NOUN
ap-9258	57	43	,	,	PUNCT
ap-9258	57	44	which	which	PRON
ap-9258	57	45	is	be	AUX
ap-9258	57	46	non	non	ADJ
ap-9258	57	47	-	-	ADJ
ap-9258	57	48	regular	regular	ADJ
ap-9258	57	49	.	.	PUNCT
ap-9258	58	1	5	5	NUM
ap-9258	58	2	×	×	NOUN
ap-9258	58	3	1	1	NUM
ap-9258	58	4	2	2	NUM
ap-9258	58	5	×	×	NOUN
ap-9258	58	6	2ap	2ap	ADJ
ap-9258	58	7	×	×	NOUN
ap-9258	58	8	ap	ap	PROPN
ap-9258	58	9	tan	tan	PROPN
ap-9258	58	10	54	54	NUM
ap-9258	58	11	=	=	NOUN
ap-9258	58	12	πac	πac	ADP
ap-9258	58	13	2	2	NUM
ap-9258	58	14	,	,	PUNCT
ap-9258	58	15	(	(	PUNCT
ap-9258	58	16	5	5	NUM
ap-9258	58	17	)	)	PUNCT
ap-9258	58	18	ap	ap	NOUN
ap-9258	58	19	=	=	PUNCT
ap-9258	58	20	(	(	PUNCT
ap-9258	58	21	√	√	PROPN
ap-9258	58	22	π	π	PROPN
ap-9258	58	23	5	5	NUM
ap-9258	58	24	tan	tan	NOUN
ap-9258	58	25	π	π	NOUN
ap-9258	58	26	5	5	NUM
ap-9258	58	27	)	)	PUNCT
ap-9258	58	28	ac	ac	PROPN
ap-9258	58	29	.	.	PUNCT
ap-9258	59	1	(	(	PUNCT
ap-9258	59	2	6	6	NUM
ap-9258	59	3	)	)	PUNCT
ap-9258	59	4	then	then	ADV
ap-9258	59	5	,	,	PUNCT
ap-9258	59	6	generally	generally	ADV
ap-9258	59	7	for	for	ADP
ap-9258	59	8	all	all	DET
ap-9258	59	9	the	the	DET
ap-9258	59	10	n	n	ADV
ap-9258	59	11	-	-	PUNCT
ap-9258	59	12	sided	sided	ADJ
ap-9258	59	13	regular	regular	ADJ
ap-9258	59	14	polygons	polygon	NOUN
ap-9258	59	15	,	,	PUNCT
ap-9258	59	16	the	the	DET
ap-9258	59	17	hsl	hsl	NOUN
ap-9258	59	18	is	be	AUX
ap-9258	59	19	:	:	PUNCT
ap-9258	59	20	∴	∴	PROPN
ap-9258	59	21	(	(	PUNCT
ap-9258	59	22	√	√	PROPN
ap-9258	59	23	π	π	PROPN
ap-9258	59	24	n	n	PRON
ap-9258	59	25	tan	tan	PROPN
ap-9258	59	26	π	π	PROPN
ap-9258	59	27	n	n	CCONJ
ap-9258	59	28	)	)	PUNCT
ap-9258	59	29	ac	ac	PROPN
ap-9258	59	30	.	.	PUNCT
ap-9258	60	1	(	(	PUNCT
ap-9258	60	2	7	7	X
ap-9258	60	3	)	)	SYM
ap-9258	60	4	3	3	NUM
ap-9258	60	5	.	.	PUNCT
ap-9258	61	1	derivation	derivation	NOUN
ap-9258	61	2	of	of	ADP
ap-9258	61	3	the	the	DET
ap-9258	61	4	directional	directional	ADJ
ap-9258	61	5	factors	factor	NOUN
ap-9258	61	6	of	of	ADP
ap-9258	61	7	the	the	DET
ap-9258	61	8	acoustic	acoustic	ADJ
ap-9258	61	9	piston	piston	NOUN
ap-9258	61	10	surfaces	surface	NOUN
ap-9258	61	11	this	this	DET
ap-9258	61	12	section	section	NOUN
ap-9258	61	13	describes	describe	VERB
ap-9258	61	14	the	the	DET
ap-9258	61	15	procedures	procedure	NOUN
ap-9258	61	16	for	for	ADP
ap-9258	61	17	the	the	DET
ap-9258	61	18	derivation	derivation	NOUN
ap-9258	61	19	of	of	ADP
ap-9258	61	20	the	the	DET
ap-9258	61	21	beam	beam	NOUN
ap-9258	61	22	patterns	pattern	NOUN
ap-9258	61	23	for	for	ADP
ap-9258	61	24	all	all	DET
ap-9258	61	25	the	the	DET
ap-9258	61	26	sources	source	NOUN
ap-9258	61	27	with	with	ADP
ap-9258	61	28	the	the	DET
ap-9258	61	29	assumption	assumption	NOUN
ap-9258	61	30	that	that	SCONJ
ap-9258	61	31	all	all	DET
ap-9258	61	32	the	the	DET
ap-9258	61	33	pistons	piston	NOUN
ap-9258	61	34	are	be	AUX
ap-9258	61	35	mounted	mount	VERB
ap-9258	61	36	on	on	ADP
ap-9258	61	37	rigid	rigid	ADJ
ap-9258	61	38	baffles	baffle	NOUN
ap-9258	61	39	.	.	PUNCT
ap-9258	62	1	471	471	NUM
ap-9258	62	2	t.	t.	PROPN
ap-9258	62	3	a.	a.	PROPN
ap-9258	62	4	yusuf	yusuf	PROPN
ap-9258	62	5	,	,	PUNCT
ap-9258	62	6	s.	s.	PROPN
ap-9258	62	7	a.	a.	PROPN
ap-9258	62	8	aodu	aodu	PROPN
ap-9258	62	9	,	,	PUNCT
ap-9258	62	10	a.	a.	NOUN
ap-9258	62	11	o.	o.	PROPN
ap-9258	62	12	alabi	alabi	PROPN
ap-9258	62	13	acta	acta	PROPN
ap-9258	62	14	polytechnica	polytechnica	PROPN
ap-9258	62	15	ac	ac	PROPN
ap-9258	62	16	figure	figure	NOUN
ap-9258	62	17	1	1	NUM
ap-9258	62	18	.	.	PUNCT
ap-9258	63	1	the	the	DET
ap-9258	63	2	reference	reference	NOUN
ap-9258	63	3	circular	circular	PROPN
ap-9258	63	4	piston	piston	NOUN
ap-9258	63	5	.	.	PUNCT
ap-9258	64	1	at	at	ADP
ap-9258	64	2	at	at	ADP
ap-9258	64	3	(	(	PUNCT
ap-9258	64	4	a	a	NOUN
ap-9258	64	5	)	)	PUNCT
ap-9258	64	6	.	.	PUNCT
ap-9258	64	7	triangle	triangle	NOUN
ap-9258	64	8	.	.	PUNCT
ap-9258	65	1	ac	ac	PROPN
ap-9258	65	2	ar	ar	PROPN
ap-9258	65	3	(	(	PUNCT
ap-9258	65	4	b	b	NOUN
ap-9258	65	5	)	)	PUNCT
ap-9258	65	6	.	.	PUNCT
ap-9258	66	1	rectangle	rectangle	NOUN
ap-9258	66	2	.	.	PUNCT
ap-9258	67	1	as	as	ADP
ap-9258	67	2	as	as	ADP
ap-9258	67	3	(	(	PUNCT
ap-9258	67	4	c	c	NOUN
ap-9258	67	5	)	)	PUNCT
ap-9258	67	6	.	.	PUNCT
ap-9258	68	1	square	square	PROPN
ap-9258	68	2	.	.	PUNCT
ap-9258	69	1	ap	ap	PROPN
ap-9258	69	2	ap	ap	PROPN
ap-9258	70	1	(	(	PUNCT
ap-9258	70	2	d	d	NOUN
ap-9258	70	3	)	)	PUNCT
ap-9258	70	4	.	.	PUNCT
ap-9258	71	1	pentagon	pentagon	PROPN
ap-9258	71	2	.	.	PUNCT
ap-9258	72	1	ax	ax	NOUN
ap-9258	72	2	ax	ax	NOUN
ap-9258	72	3	(	(	PUNCT
ap-9258	72	4	e	e	NOUN
ap-9258	72	5	)	)	PUNCT
ap-9258	72	6	.	.	PUNCT
ap-9258	73	1	hexagon	hexagon	PROPN
ap-9258	73	2	.	.	PUNCT
ap-9258	74	1	ah	ah	INTJ
ap-9258	74	2	ah	ah	INTJ
ap-9258	74	3	(	(	PUNCT
ap-9258	74	4	f	f	NOUN
ap-9258	74	5	)	)	PUNCT
ap-9258	74	6	.	.	PUNCT
ap-9258	75	1	heptagon	heptagon	PROPN
ap-9258	75	2	.	.	PUNCT
ap-9258	76	1	ao	ao	PROPN
ap-9258	76	2	ao	ao	PROPN
ap-9258	76	3	(	(	PUNCT
ap-9258	76	4	g	g	NOUN
ap-9258	76	5	)	)	PUNCT
ap-9258	76	6	.	.	PUNCT
ap-9258	77	1	octagon	octagon	PROPN
ap-9258	77	2	.	.	PUNCT
ap-9258	78	1	an	an	DET
ap-9258	78	2	an	an	DET
ap-9258	78	3	(	(	PUNCT
ap-9258	78	4	h	h	NOUN
ap-9258	78	5	)	)	PUNCT
ap-9258	78	6	.	.	PUNCT
ap-9258	79	1	nonagon	nonagon	ADJ
ap-9258	79	2	.	.	PUNCT
ap-9258	80	1	ad	ad	NOUN
ap-9258	80	2	ad	ad	NOUN
ap-9258	80	3	(	(	PUNCT
ap-9258	80	4	i	i	NOUN
ap-9258	80	5	)	)	PUNCT
ap-9258	80	6	.	.	PUNCT
ap-9258	81	1	decagon	decagon	PROPN
ap-9258	81	2	.	.	PUNCT
ap-9258	82	1	figure	figure	NOUN
ap-9258	82	2	2	2	NUM
ap-9258	82	3	.	.	PUNCT
ap-9258	83	1	the	the	DET
ap-9258	83	2	polygonal	polygonal	ADJ
ap-9258	83	3	piston	piston	NOUN
ap-9258	83	4	surfaces	surface	NOUN
ap-9258	83	5	.	.	PUNCT
ap-9258	84	1	472	472	NUM
ap-9258	84	2	vol	vol	NOUN
ap-9258	84	3	.	.	PUNCT
ap-9258	85	1	64	64	NUM
ap-9258	85	2	no	no	NOUN
ap-9258	85	3	.	.	PUNCT
ap-9258	86	1	5/2024	5/2024	ADJ
ap-9258	86	2	acoustic	acoustic	ADJ
ap-9258	86	3	radiation	radiation	NOUN
ap-9258	86	4	beam	beam	NOUN
ap-9258	86	5	patterns	pattern	NOUN
ap-9258	86	6	of	of	ADP
ap-9258	86	7	different	different	ADJ
ap-9258	86	8	polygonal	polygonal	NOUN
ap-9258	86	9	.	.	PUNCT
ap-9258	86	10	.	.	PUNCT
ap-9258	86	11	.	.	PUNCT
ap-9258	87	1	2ap	2ap	NOUN
ap-9258	87	2	54o	54o	NOUN
ap-9258	87	3	72o	72o	NOUN
ap-9258	87	4	figure	figure	VERB
ap-9258	87	5	3	3	NUM
ap-9258	87	6	.	.	PUNCT
ap-9258	88	1	the	the	DET
ap-9258	88	2	pentagon	pentagon	PROPN
ap-9258	88	3	surface	surface	PROPN
ap-9258	88	4	area	area	PROPN
ap-9258	88	5	geometry	geometry	NOUN
ap-9258	88	6	.	.	PUNCT
ap-9258	89	1	3.1	3.1	NUM
ap-9258	89	2	.	.	PUNCT
ap-9258	89	3	circular	circular	ADJ
ap-9258	89	4	piston	piston	NOUN
ap-9258	89	5	the	the	DET
ap-9258	89	6	directional	directional	ADJ
ap-9258	89	7	factor	factor	NOUN
ap-9258	89	8	of	of	ADP
ap-9258	89	9	a	a	DET
ap-9258	89	10	circular	circular	ADJ
ap-9258	89	11	piston	piston	NOUN
ap-9258	89	12	on	on	ADP
ap-9258	89	13	a	a	DET
ap-9258	89	14	rigid	rigid	ADJ
ap-9258	89	15	baffle	baffle	NOUN
ap-9258	89	16	is	be	AUX
ap-9258	89	17	well	well	ADV
ap-9258	89	18	known	known	ADJ
ap-9258	89	19	[	[	X
ap-9258	89	20	24	24	NUM
ap-9258	89	21	]	]	PUNCT
ap-9258	89	22	.	.	PUNCT
ap-9258	90	1	however	however	ADV
ap-9258	90	2	,	,	PUNCT
ap-9258	90	3	it	it	PRON
ap-9258	90	4	would	would	AUX
ap-9258	90	5	be	be	AUX
ap-9258	90	6	derived	derive	VERB
ap-9258	90	7	again	again	ADV
ap-9258	90	8	in	in	ADP
ap-9258	90	9	this	this	DET
ap-9258	90	10	study	study	NOUN
ap-9258	90	11	to	to	PART
ap-9258	90	12	set	set	VERB
ap-9258	90	13	a	a	DET
ap-9258	90	14	general	general	ADJ
ap-9258	90	15	background	background	NOUN
ap-9258	90	16	for	for	SCONJ
ap-9258	90	17	the	the	DET
ap-9258	90	18	approach	approach	NOUN
ap-9258	90	19	to	to	PART
ap-9258	90	20	be	be	AUX
ap-9258	90	21	used	use	VERB
ap-9258	90	22	for	for	ADP
ap-9258	90	23	the	the	DET
ap-9258	90	24	polygons	polygon	NOUN
ap-9258	90	25	.	.	PUNCT
ap-9258	91	1	consider	consider	VERB
ap-9258	91	2	an	an	DET
ap-9258	91	3	acoustic	acoustic	ADJ
ap-9258	91	4	element	element	NOUN
ap-9258	91	5	of	of	ADP
ap-9258	91	6	a	a	DET
ap-9258	91	7	hsl	hsl	NOUN
ap-9258	91	8	,	,	PUNCT
ap-9258	91	9	ab	ab	PROPN
ap-9258	91	10	and	and	CCONJ
ap-9258	91	11	a	a	DET
ap-9258	91	12	small	small	ADJ
ap-9258	91	13	thickness	thickness	NOUN
ap-9258	91	14	dx	dx	PROPN
ap-9258	91	15	whose	whose	DET
ap-9258	91	16	centre	centre	NOUN
ap-9258	91	17	a	a	PRON
ap-9258	91	18	is	be	AUX
ap-9258	91	19	located	locate	VERB
ap-9258	91	20	at	at	ADP
ap-9258	91	21	distance	distance	NOUN
ap-9258	91	22	x	x	PUNCT
ap-9258	91	23	from	from	ADP
ap-9258	91	24	the	the	DET
ap-9258	91	25	centre	centre	NOUN
ap-9258	91	26	c	c	PROPN
ap-9258	91	27	of	of	ADP
ap-9258	91	28	the	the	DET
ap-9258	91	29	circular	circular	ADJ
ap-9258	91	30	piston	piston	NOUN
ap-9258	91	31	as	as	SCONJ
ap-9258	91	32	shown	show	VERB
ap-9258	91	33	in	in	ADP
ap-9258	91	34	figure	figure	NOUN
ap-9258	91	35	4	4	NUM
ap-9258	91	36	.	.	PUNCT
ap-9258	92	1	the	the	DET
ap-9258	92	2	piston	piston	NOUN
ap-9258	92	3	is	be	AUX
ap-9258	92	4	considered	consider	VERB
ap-9258	92	5	to	to	PART
ap-9258	92	6	be	be	AUX
ap-9258	92	7	on	on	ADP
ap-9258	92	8	a	a	DET
ap-9258	92	9	rigid	rigid	ADJ
ap-9258	92	10	baffle	baffle	NOUN
ap-9258	92	11	such	such	ADJ
ap-9258	92	12	that	that	SCONJ
ap-9258	92	13	acoustic	acoustic	ADJ
ap-9258	92	14	radiation	radiation	NOUN
ap-9258	92	15	is	be	AUX
ap-9258	92	16	projected	project	VERB
ap-9258	92	17	in	in	ADP
ap-9258	92	18	the	the	DET
ap-9258	92	19	forward	forward	ADJ
ap-9258	92	20	direction	direction	NOUN
ap-9258	92	21	from	from	ADP
ap-9258	92	22	its	its	PRON
ap-9258	92	23	surface	surface	NOUN
ap-9258	92	24	into	into	ADP
ap-9258	92	25	a	a	DET
ap-9258	92	26	point	point	NOUN
ap-9258	92	27	q	q	NOUN
ap-9258	92	28	at	at	ADP
ap-9258	92	29	an	an	DET
ap-9258	92	30	angle	angle	NOUN
ap-9258	92	31	θ	θ	NOUN
ap-9258	92	32	from	from	ADP
ap-9258	92	33	the	the	DET
ap-9258	92	34	vertical	vertical	ADJ
ap-9258	92	35	acoustic	acoustic	ADJ
ap-9258	92	36	axis	axis	NOUN
ap-9258	92	37	.	.	PUNCT
ap-9258	93	1	point	point	NOUN
ap-9258	93	2	q	q	NOUN
ap-9258	93	3	is	be	AUX
ap-9258	93	4	located	locate	VERB
ap-9258	93	5	at	at	ADP
ap-9258	93	6	distances	distance	NOUN
ap-9258	93	7	r	r	NOUN
ap-9258	93	8	and	and	CCONJ
ap-9258	93	9	r	r	NOUN
ap-9258	93	10	from	from	ADP
ap-9258	93	11	the	the	DET
ap-9258	93	12	centres	centre	NOUN
ap-9258	93	13	c	c	PROPN
ap-9258	93	14	and	and	CCONJ
ap-9258	93	15	a	a	PRON
ap-9258	93	16	,	,	PUNCT
ap-9258	93	17	respectively	respectively	ADV
ap-9258	93	18	.	.	PUNCT
ap-9258	94	1	taking	take	VERB
ap-9258	94	2	ap	ap	PROPN
ap-9258	94	3	as	as	ADP
ap-9258	94	4	a	a	DET
ap-9258	94	5	wave	wave	NOUN
ap-9258	94	6	front	front	ADJ
ap-9258	94	7	perpendicular	perpendicular	NOUN
ap-9258	94	8	to	to	ADP
ap-9258	94	9	cq	cq	PROPN
ap-9258	94	10	,	,	PUNCT
ap-9258	94	11	the	the	DET
ap-9258	94	12	relationship	relationship	NOUN
ap-9258	94	13	between	between	ADP
ap-9258	94	14	cp	cp	PROPN
ap-9258	94	15	and	and	CCONJ
ap-9258	94	16	x	x	PRON
ap-9258	94	17	can	can	AUX
ap-9258	94	18	be	be	AUX
ap-9258	94	19	found	find	VERB
ap-9258	94	20	as	as	SCONJ
ap-9258	94	21	expressed	express	VERB
ap-9258	94	22	in	in	ADP
ap-9258	94	23	equation	equation	NOUN
ap-9258	94	24	(	(	PUNCT
ap-9258	94	25	8)	8)	NUM
ap-9258	94	26	.	.	PUNCT
ap-9258	95	1	considering	consider	VERB
ap-9258	95	2	that	that	SCONJ
ap-9258	95	3	r	r	NOUN
ap-9258	95	4	and	and	CCONJ
ap-9258	95	5	r	r	NOUN
ap-9258	95	6	are	be	AUX
ap-9258	95	7	distances	distance	NOUN
ap-9258	95	8	in	in	ADP
ap-9258	95	9	the	the	DET
ap-9258	95	10	far	far	ADV
ap-9258	95	11	-	-	PUNCT
ap-9258	95	12	field	field	NOUN
ap-9258	95	13	,	,	PUNCT
ap-9258	95	14	the	the	DET
ap-9258	95	15	line	line	NOUN
ap-9258	95	16	cq	cq	PROPN
ap-9258	95	17	and	and	CCONJ
ap-9258	95	18	aq	aq	PROPN
ap-9258	95	19	are	be	AUX
ap-9258	95	20	parallel	parallel	VERB
ap-9258	95	21	resulting	result	VERB
ap-9258	95	22	into	into	ADP
ap-9258	95	23	equation	equation	NOUN
ap-9258	95	24	(	(	PUNCT
ap-9258	95	25	9	9	NUM
ap-9258	95	26	)	)	PUNCT
ap-9258	95	27	.	.	PUNCT
ap-9258	96	1	cp	cp	X
ap-9258	97	1	=	=	PUNCT
ap-9258	97	2	x	x	PROPN
ap-9258	97	3	sin	sin	PROPN
ap-9258	97	4	θ	θ	PROPN
ap-9258	97	5	,	,	PUNCT
ap-9258	97	6	(	(	PUNCT
ap-9258	97	7	8)	8)	NUM
ap-9258	97	8	r	r	NOUN
ap-9258	97	9	=	=	SYM
ap-9258	97	10	r	r	NOUN
ap-9258	97	11	−	−	NOUN
ap-9258	98	1	cp	cp	INTJ
ap-9258	98	2	=	=	SYM
ap-9258	98	3	r	r	NOUN
ap-9258	98	4	−	−	NOUN
ap-9258	98	5	x	x	PUNCT
ap-9258	98	6	sin	sin	NOUN
ap-9258	98	7	θ	θ	PROPN
ap-9258	98	8	.	.	PUNCT
ap-9258	99	1	(	(	PUNCT
ap-9258	99	2	9	9	X
ap-9258	99	3	)	)	PUNCT
ap-9258	99	4	the	the	DET
ap-9258	99	5	total	total	ADJ
ap-9258	99	6	acoustic	acoustic	ADJ
ap-9258	99	7	pressure	pressure	NOUN
ap-9258	99	8	radiated	radiate	VERB
ap-9258	99	9	from	from	ADP
ap-9258	99	10	the	the	DET
ap-9258	99	11	acoustic	acoustic	ADJ
ap-9258	99	12	element	element	NOUN
ap-9258	99	13	,	,	PUNCT
ap-9258	99	14	pc	pc	NOUN
ap-9258	99	15	can	can	AUX
ap-9258	99	16	be	be	AUX
ap-9258	99	17	calculated	calculate	VERB
ap-9258	99	18	using	use	VERB
ap-9258	99	19	the	the	DET
ap-9258	99	20	rayleigh	rayleigh	PROPN
ap-9258	99	21	integral	integral	ADJ
ap-9258	99	22	over	over	ADP
ap-9258	99	23	the	the	DET
ap-9258	99	24	entire	entire	ADJ
ap-9258	99	25	region	region	NOUN
ap-9258	99	26	of	of	ADP
ap-9258	99	27	the	the	DET
ap-9258	99	28	piston	piston	NOUN
ap-9258	99	29	surface	surface	NOUN
ap-9258	99	30	as	as	SCONJ
ap-9258	99	31	expressed	express	VERB
ap-9258	99	32	in	in	ADP
ap-9258	99	33	equation	equation	NOUN
ap-9258	99	34	(	(	PUNCT
ap-9258	99	35	10	10	NUM
ap-9258	99	36	)	)	PUNCT
ap-9258	99	37	.	.	PUNCT
ap-9258	100	1	in	in	ADP
ap-9258	100	2	this	this	DET
ap-9258	100	3	equation	equation	NOUN
ap-9258	100	4	,	,	PUNCT
ap-9258	100	5	a	a	PRON
ap-9258	100	6	is	be	AUX
ap-9258	100	7	a	a	DET
ap-9258	100	8	constant	constant	ADJ
ap-9258	100	9	which	which	PRON
ap-9258	100	10	depends	depend	VERB
ap-9258	100	11	on	on	ADP
ap-9258	100	12	certain	certain	ADJ
ap-9258	100	13	properties	property	NOUN
ap-9258	100	14	of	of	ADP
ap-9258	100	15	the	the	DET
ap-9258	100	16	medium	medium	NOUN
ap-9258	100	17	,	,	PUNCT
ap-9258	100	18	namely	namely	ADV
ap-9258	100	19	the	the	DET
ap-9258	100	20	wave	wave	NOUN
ap-9258	100	21	and	and	CCONJ
ap-9258	100	22	the	the	DET
ap-9258	100	23	acoustic	acoustic	ADJ
ap-9258	100	24	element	element	NOUN
ap-9258	100	25	.	.	PUNCT
ap-9258	101	1	ω	ω	PROPN
ap-9258	101	2	is	be	AUX
ap-9258	101	3	the	the	DET
ap-9258	101	4	angular	angular	ADJ
ap-9258	101	5	frequency	frequency	NOUN
ap-9258	101	6	,	,	PUNCT
ap-9258	101	7	k	k	PROPN
ap-9258	101	8	is	be	AUX
ap-9258	101	9	the	the	DET
ap-9258	101	10	wave	wave	NOUN
ap-9258	101	11	constant	constant	ADJ
ap-9258	101	12	and	and	CCONJ
ap-9258	101	13	t	t	PROPN
ap-9258	101	14	is	be	AUX
ap-9258	101	15	the	the	DET
ap-9258	101	16	time	time	NOUN
ap-9258	101	17	of	of	ADP
ap-9258	101	18	wave	wave	NOUN
ap-9258	101	19	propagation	propagation	NOUN
ap-9258	101	20	.	.	PUNCT
ap-9258	102	1	ds	ds	PROPN
ap-9258	102	2	is	be	AUX
ap-9258	102	3	the	the	DET
ap-9258	102	4	cross	cross	ADJ
ap-9258	102	5	-	-	ADJ
ap-9258	102	6	sectional	sectional	ADJ
ap-9258	102	7	surface	surface	NOUN
ap-9258	102	8	area	area	NOUN
ap-9258	102	9	of	of	ADP
ap-9258	102	10	the	the	DET
ap-9258	102	11	element	element	NOUN
ap-9258	102	12	calculated	calculate	VERB
ap-9258	102	13	as	as	ADP
ap-9258	102	14	the	the	DET
ap-9258	102	15	product	product	NOUN
ap-9258	102	16	of	of	ADP
ap-9258	102	17	the	the	DET
ap-9258	102	18	total	total	ADJ
ap-9258	102	19	length	length	NOUN
ap-9258	102	20	and	and	CCONJ
ap-9258	102	21	thickness	thickness	NOUN
ap-9258	102	22	dx	dx	PROPN
ap-9258	102	23	,	,	PUNCT
ap-9258	102	24	i.e.	i.e.	X
ap-9258	102	25	2(ab)dx	2(ab)dx	NOUN
ap-9258	102	26	.	.	PUNCT
ap-9258	103	1	determining	determine	VERB
ap-9258	103	2	ab	ab	PROPN
ap-9258	103	3	from	from	ADP
ap-9258	103	4	figure	figure	NOUN
ap-9258	103	5	4	4	NUM
ap-9258	103	6	,	,	PUNCT
ap-9258	103	7	ds	ds	X
ap-9258	103	8	can	can	AUX
ap-9258	103	9	be	be	AUX
ap-9258	103	10	expressed	express	VERB
ap-9258	103	11	as	as	SCONJ
ap-9258	103	12	shown	show	VERB
ap-9258	103	13	in	in	ADP
ap-9258	103	14	equation	equation	NOUN
ap-9258	103	15	(	(	PUNCT
ap-9258	103	16	11	11	NUM
ap-9258	103	17	)	)	PUNCT
ap-9258	103	18	.	.	PUNCT
ap-9258	104	1	pc	pc	NOUN
ap-9258	105	1	=	=	PUNCT
ap-9258	106	1	i	i	PRON
ap-9258	106	2	∫	∫	PROPN
ap-9258	106	3	ac	ac	PROPN
ap-9258	107	1	−ac	−ac	PROPN
ap-9258	107	2	a	a	DET
ap-9258	107	3	r	r	NOUN
ap-9258	107	4	ei(ωt−kr)ds	ei(ωt−kr)d	NOUN
ap-9258	107	5	,	,	PUNCT
ap-9258	107	6	(	(	PUNCT
ap-9258	107	7	10	10	NUM
ap-9258	107	8	)	)	PUNCT
ap-9258	107	9	ds	ds	NOUN
ap-9258	107	10	=	=	SYM
ap-9258	107	11	2	2	NUM
ap-9258	107	12	×	×	NOUN
ap-9258	107	13	ab	ab	PROPN
ap-9258	107	14	×	×	NOUN
ap-9258	107	15	dx	dx	PROPN
ap-9258	107	16	=	=	SYM
ap-9258	107	17	2	2	NUM
ap-9258	107	18	√	√	NUM
ap-9258	107	19	ac	ac	ADJ
ap-9258	107	20	2	2	NUM
ap-9258	107	21	−	−	NOUN
ap-9258	107	22	x2dx	x2dx	PUNCT
ap-9258	107	23	.	.	PUNCT
ap-9258	108	1	(	(	PUNCT
ap-9258	108	2	11	11	X
ap-9258	108	3	)	)	PUNCT
ap-9258	108	4	substituting	substitute	VERB
ap-9258	108	5	equations	equation	NOUN
ap-9258	108	6	(	(	PUNCT
ap-9258	108	7	9	9	NUM
ap-9258	108	8	)	)	PUNCT
ap-9258	108	9	and	and	CCONJ
ap-9258	108	10	(	(	PUNCT
ap-9258	108	11	11	11	NUM
ap-9258	108	12	)	)	PUNCT
ap-9258	108	13	in	in	ADP
ap-9258	108	14	equation	equation	NOUN
ap-9258	108	15	(	(	PUNCT
ap-9258	108	16	10	10	NUM
ap-9258	108	17	)	)	PUNCT
ap-9258	108	18	while	while	SCONJ
ap-9258	108	19	applying	apply	VERB
ap-9258	108	20	the	the	DET
ap-9258	108	21	condition	condition	NOUN
ap-9258	108	22	that	that	PRON
ap-9258	108	23	point	point	NOUN
ap-9258	108	24	q	q	NOUN
ap-9258	108	25	is	be	AUX
ap-9258	108	26	at	at	ADP
ap-9258	108	27	the	the	DET
ap-9258	108	28	far	far	ADJ
ap-9258	108	29	-	-	PUNCT
ap-9258	108	30	field	field	NOUN
ap-9258	108	31	distance	distance	NOUN
ap-9258	108	32	,	,	PUNCT
ap-9258	108	33	i.e.	i.e.	X
ap-9258	108	34	1	1	NUM
ap-9258	108	35	r	r	NOUN
ap-9258	108	36	≈	≈	PROPN
ap-9258	108	37	1	1	NUM
ap-9258	108	38	r	r	NOUN
ap-9258	108	39	,	,	PUNCT
ap-9258	108	40	the	the	DET
ap-9258	108	41	constant	constant	ADJ
ap-9258	108	42	amplitude	amplitude	NOUN
ap-9258	108	43	is	be	AUX
ap-9258	108	44	taken	take	VERB
ap-9258	108	45	out	out	ADP
ap-9258	108	46	and	and	CCONJ
ap-9258	108	47	pc	pc	NOUN
ap-9258	108	48	takes	take	VERB
ap-9258	108	49	the	the	DET
ap-9258	108	50	form	form	NOUN
ap-9258	108	51	of	of	ADP
ap-9258	108	52	equation	equation	NOUN
ap-9258	108	53	(	(	PUNCT
ap-9258	108	54	12	12	NUM
ap-9258	108	55	)	)	PUNCT
ap-9258	108	56	.	.	PUNCT
ap-9258	109	1	considering	consider	VERB
ap-9258	109	2	only	only	ADV
ap-9258	109	3	the	the	DET
ap-9258	109	4	real	real	ADJ
ap-9258	109	5	part	part	NOUN
ap-9258	109	6	of	of	ADP
ap-9258	109	7	the	the	DET
ap-9258	109	8	exponents	exponent	NOUN
ap-9258	109	9	under	under	ADP
ap-9258	109	10	the	the	DET
ap-9258	109	11	integral	integral	NOUN
ap-9258	109	12	to	to	PART
ap-9258	109	13	preserve	preserve	VERB
ap-9258	109	14	the	the	DET
ap-9258	109	15	pressure	pressure	NOUN
ap-9258	109	16	as	as	ADP
ap-9258	109	17	a	a	DET
ap-9258	109	18	complex	complex	ADJ
ap-9258	109	19	component	component	NOUN
ap-9258	109	20	of	of	ADP
ap-9258	109	21	the	the	DET
ap-9258	109	22	whole	whole	ADJ
ap-9258	109	23	expression	expression	NOUN
ap-9258	109	24	,	,	PUNCT
ap-9258	109	25	equation	equation	NOUN
ap-9258	109	26	(	(	PUNCT
ap-9258	109	27	13	13	NUM
ap-9258	109	28	)	)	PUNCT
ap-9258	109	29	is	be	AUX
ap-9258	109	30	obtained	obtain	VERB
ap-9258	109	31	.	.	PUNCT
ap-9258	110	1	if	if	SCONJ
ap-9258	110	2	x	x	PRON
ap-9258	110	3	is	be	AUX
ap-9258	110	4	set	set	VERB
ap-9258	110	5	to	to	ADP
ap-9258	110	6	ac	ac	PROPN
ap-9258	110	7	cos	cos	PROPN
ap-9258	110	8	θ	θ	PROPN
ap-9258	110	9	the	the	DET
ap-9258	110	10	integral	integral	ADJ
ap-9258	110	11	is	be	AUX
ap-9258	110	12	transformed	transform	VERB
ap-9258	110	13	into	into	ADP
ap-9258	110	14	equation	equation	NOUN
ap-9258	110	15	(	(	PUNCT
ap-9258	110	16	14	14	NUM
ap-9258	110	17	)	)	PUNCT
ap-9258	110	18	,	,	PUNCT
ap-9258	110	19	which	which	PRON
ap-9258	110	20	is	be	AUX
ap-9258	110	21	simplified	simplify	VERB
ap-9258	110	22	where	where	SCONJ
ap-9258	110	23	j1	j1	PROPN
ap-9258	110	24	is	be	AUX
ap-9258	110	25	a	a	DET
ap-9258	110	26	bessel	bessel	NOUN
ap-9258	110	27	’s	’s	PART
ap-9258	110	28	function	function	NOUN
ap-9258	110	29	of	of	ADP
ap-9258	110	30	the	the	DET
ap-9258	110	31	first	first	ADJ
ap-9258	110	32	kind	kind	NOUN
ap-9258	110	33	as	as	SCONJ
ap-9258	110	34	shown	show	VERB
ap-9258	110	35	in	in	ADP
ap-9258	110	36	[	[	X
ap-9258	110	37	25	25	NUM
ap-9258	110	38	]	]	PUNCT
ap-9258	110	39	.	.	PUNCT
ap-9258	111	1	the	the	DET
ap-9258	111	2	directional	directional	ADJ
ap-9258	111	3	factor	factor	NOUN
ap-9258	111	4	hc	hc	PROPN
ap-9258	111	5	is	be	AUX
ap-9258	111	6	the	the	DET
ap-9258	111	7	absolute	absolute	ADJ
ap-9258	111	8	value	value	NOUN
ap-9258	111	9	of	of	ADP
ap-9258	111	10	the	the	DET
ap-9258	111	11	angular	angular	ADJ
ap-9258	111	12	component	component	NOUN
ap-9258	111	13	isolated	isolate	VERB
ap-9258	111	14	as	as	SCONJ
ap-9258	111	15	expressed	express	VERB
ap-9258	111	16	in	in	ADP
ap-9258	111	17	equation	equation	NOUN
ap-9258	111	18	(	(	PUNCT
ap-9258	111	19	15	15	NUM
ap-9258	111	20	)	)	PUNCT
ap-9258	111	21	.	.	PUNCT
ap-9258	112	1	using	use	VERB
ap-9258	112	2	the	the	DET
ap-9258	112	3	same	same	ADJ
ap-9258	112	4	approach	approach	NOUN
ap-9258	112	5	,	,	PUNCT
ap-9258	112	6	directional	directional	ADJ
ap-9258	112	7	factors	factor	NOUN
ap-9258	112	8	of	of	ADP
ap-9258	112	9	other	other	ADJ
ap-9258	112	10	surfaces	surface	NOUN
ap-9258	112	11	would	would	AUX
ap-9258	112	12	be	be	AUX
ap-9258	112	13	derived	derive	VERB
ap-9258	112	14	accordingly	accordingly	ADV
ap-9258	112	15	in	in	ADP
ap-9258	112	16	their	their	PRON
ap-9258	112	17	respective	respective	ADJ
ap-9258	112	18	sections	section	NOUN
ap-9258	112	19	.	.	PUNCT
ap-9258	113	1	the	the	DET
ap-9258	113	2	major	major	ADJ
ap-9258	113	3	difference	difference	NOUN
ap-9258	113	4	in	in	ADP
ap-9258	113	5	the	the	DET
ap-9258	113	6	analytical	analytical	ADJ
ap-9258	113	7	procedure	procedure	NOUN
ap-9258	113	8	is	be	AUX
ap-9258	113	9	the	the	DET
ap-9258	113	10	determination	determination	NOUN
ap-9258	113	11	of	of	ADP
ap-9258	113	12	the	the	DET
ap-9258	113	13	hsl	hsl	NOUN
ap-9258	113	14	,	,	PUNCT
ap-9258	113	15	ab	ab	PROPN
ap-9258	113	16	for	for	ADP
ap-9258	113	17	each	each	DET
ap-9258	113	18	surface	surface	NOUN
ap-9258	113	19	.	.	PUNCT
ap-9258	114	1	pc	pc	NOUN
ap-9258	115	1	=	=	PRON
ap-9258	115	2	i	i	PRON
ap-9258	115	3	a	a	DET
ap-9258	115	4	r	r	NOUN
ap-9258	115	5	2ei(ωt−kr	2ei(ωt−kr	NUM
ap-9258	115	6	)	)	PUNCT
ap-9258	116	1	∫	∫	PROPN
ap-9258	117	1	ac	ac	PROPN
ap-9258	118	1	−ac	−ac	PROPN
ap-9258	118	2	eikx	eikx	PROPN
ap-9258	118	3	sin	sin	NOUN
ap-9258	118	4	θ	θ	PROPN
ap-9258	118	5	√	√	NOUN
ap-9258	118	6	ac	ac	ADJ
ap-9258	118	7	2	2	NUM
ap-9258	118	8	−	−	NOUN
ap-9258	118	9	x2dx	x2dx	SYM
ap-9258	118	10	,	,	PUNCT
ap-9258	118	11	(	(	PUNCT
ap-9258	118	12	12	12	NUM
ap-9258	118	13	)	)	PUNCT
ap-9258	118	14	pc	pc	NOUN
ap-9258	119	1	=	=	NOUN
ap-9258	119	2	i	i	PRON
ap-9258	119	3	a	a	DET
ap-9258	119	4	r	r	NOUN
ap-9258	119	5	2ei(ωt−kr	2ei(ωt−kr	NUM
ap-9258	119	6	)	)	PUNCT
ap-9258	120	1	∫	∫	PROPN
ap-9258	120	2	ac	ac	PROPN
ap-9258	120	3	−ac	−ac	PROPN
ap-9258	120	4	cos	cos	PROPN
ap-9258	120	5	(	(	PUNCT
ap-9258	120	6	kx	kx	PROPN
ap-9258	120	7	sin	sin	PROPN
ap-9258	120	8	θ	θ	PROPN
ap-9258	120	9	)	)	PUNCT
ap-9258	120	10	√	√	NOUN
ap-9258	120	11	ac	ac	ADJ
ap-9258	120	12	2	2	NUM
ap-9258	120	13	−	−	NOUN
ap-9258	120	14	x2dx	x2dx	SYM
ap-9258	120	15	,	,	PUNCT
ap-9258	120	16	(	(	PUNCT
ap-9258	120	17	13	13	NUM
ap-9258	120	18	)	)	PUNCT
ap-9258	120	19	pc	pc	NOUN
ap-9258	121	1	=	=	NOUN
ap-9258	121	2	i	i	PRON
ap-9258	121	3	a	a	DET
ap-9258	121	4	r	r	NOUN
ap-9258	121	5	2ac	2ac	PROPN
ap-9258	121	6	2ei(ωt−kr	2ei(ωt−kr	PROPN
ap-9258	121	7	)	)	PUNCT
ap-9258	122	1	∫	∫	PROPN
ap-9258	123	1	π	π	PROPN
ap-9258	123	2	0	0	PUNCT
ap-9258	123	3	cos	cos	PROPN
ap-9258	123	4	(	(	PUNCT
ap-9258	123	5	kac	kac	PROPN
ap-9258	123	6	cos	cos	PROPN
ap-9258	123	7	θ	θ	PROPN
ap-9258	123	8	sin	sin	NOUN
ap-9258	123	9	θ	θ	PROPN
ap-9258	123	10	)	)	PUNCT
ap-9258	123	11	sin2	sin2	NOUN
ap-9258	123	12	θdθ	θdθ	NOUN
ap-9258	124	1	=	=	PRON
ap-9258	124	2	i	i	PRON
ap-9258	124	3	a	a	DET
ap-9258	124	4	r	r	NOUN
ap-9258	124	5	2πac	2πac	NUM
ap-9258	124	6	2ei(ωt−kr	2ei(ωt−kr	NUM
ap-9258	124	7	)	)	PUNCT
ap-9258	124	8	j1	j1	PROPN
ap-9258	124	9	(	(	PUNCT
ap-9258	124	10	kac	kac	PROPN
ap-9258	124	11	sin	sin	PROPN
ap-9258	124	12	θ	θ	PROPN
ap-9258	124	13	)	)	PUNCT
ap-9258	124	14	kac	kac	PROPN
ap-9258	124	15	sin	sin	PROPN
ap-9258	124	16	θ	θ	PROPN
ap-9258	124	17	,	,	PUNCT
ap-9258	124	18	(	(	PUNCT
ap-9258	124	19	14	14	NUM
ap-9258	124	20	)	)	PUNCT
ap-9258	124	21	hc	hc	PROPN
ap-9258	124	22	(	(	PUNCT
ap-9258	124	23	θ	θ	NOUN
ap-9258	124	24	)	)	PUNCT
ap-9258	124	25	=	=	VERB
ap-9258	124	26	∣∣∣∣2j1	∣∣∣∣2j1	NOUN
ap-9258	124	27	(	(	PUNCT
ap-9258	124	28	kac	kac	PROPN
ap-9258	124	29	sin	sin	PROPN
ap-9258	124	30	θ	θ	PROPN
ap-9258	124	31	)	)	PUNCT
ap-9258	124	32	kac	kac	PROPN
ap-9258	125	1	sin	sin	PROPN
ap-9258	125	2	θ	θ	PROPN
ap-9258	125	3	∣∣∣∣.	∣∣∣∣.	PROPN
ap-9258	125	4	(	(	PUNCT
ap-9258	125	5	15	15	NUM
ap-9258	125	6	)	)	PUNCT
ap-9258	125	7	473	473	NUM
ap-9258	125	8	t.	t.	NOUN
ap-9258	125	9	a.	a.	PROPN
ap-9258	125	10	yusuf	yusuf	PROPN
ap-9258	125	11	,	,	PUNCT
ap-9258	125	12	s.	s.	PROPN
ap-9258	125	13	a.	a.	PROPN
ap-9258	125	14	aodu	aodu	PROPN
ap-9258	125	15	,	,	PUNCT
ap-9258	125	16	a.	a.	NOUN
ap-9258	125	17	o.	o.	NOUN
ap-9258	125	18	alabi	alabi	PROPN
ap-9258	125	19	acta	acta	PROPN
ap-9258	125	20	polytechnica	polytechnica	PROPN
ap-9258	125	21	q	q	PROPN
ap-9258	125	22	c	c	PROPN
ap-9258	126	1	a	a	PRON
ap-9258	126	2	y	y	NOUN
ap-9258	126	3	x	x	SYM
ap-9258	126	4	θ	θ	NOUN
ap-9258	126	5	ac	ac	PROPN
ap-9258	127	1	p	p	X
ap-9258	127	2	b	b	PROPN
ap-9258	127	3	r	r	NOUN
ap-9258	127	4	r	r	NOUN
ap-9258	127	5	z	z	NOUN
ap-9258	127	6	figure	figure	NOUN
ap-9258	127	7	4	4	NUM
ap-9258	127	8	.	.	PUNCT
ap-9258	128	1	the	the	DET
ap-9258	128	2	surface	surface	NOUN
ap-9258	128	3	geometry	geometry	NOUN
ap-9258	128	4	for	for	ADP
ap-9258	128	5	the	the	DET
ap-9258	128	6	derivation	derivation	NOUN
ap-9258	128	7	of	of	ADP
ap-9258	128	8	the	the	DET
ap-9258	128	9	directional	directional	ADJ
ap-9258	128	10	factor	factor	NOUN
ap-9258	128	11	of	of	ADP
ap-9258	128	12	a	a	DET
ap-9258	128	13	circular	circular	ADJ
ap-9258	128	14	piston	piston	NOUN
ap-9258	128	15	.	.	PUNCT
ap-9258	129	1	3.2	3.2	NUM
ap-9258	129	2	.	.	X
ap-9258	129	3	triangular	triangular	NOUN
ap-9258	129	4	piston	piston	NOUN
ap-9258	129	5	for	for	ADP
ap-9258	129	6	the	the	DET
ap-9258	129	7	triangle	triangle	NOUN
ap-9258	129	8	piston	piston	NOUN
ap-9258	129	9	,	,	PUNCT
ap-9258	129	10	the	the	DET
ap-9258	129	11	centre	centre	NOUN
ap-9258	129	12	c	c	PROPN
ap-9258	129	13	is	be	AUX
ap-9258	129	14	located	locate	VERB
ap-9258	129	15	from	from	ADP
ap-9258	129	16	the	the	DET
ap-9258	129	17	base	base	NOUN
ap-9258	129	18	and	and	CCONJ
ap-9258	129	19	top	top	NOUN
ap-9258	129	20	of	of	ADP
ap-9258	129	21	the	the	DET
ap-9258	129	22	surface	surface	NOUN
ap-9258	129	23	as	as	SCONJ
ap-9258	129	24	shown	show	VERB
ap-9258	129	25	in	in	ADP
ap-9258	129	26	figure	figure	NOUN
ap-9258	129	27	5	5	NUM
ap-9258	129	28	.	.	PUNCT
ap-9258	130	1	the	the	DET
ap-9258	130	2	point	point	NOUN
ap-9258	130	3	c	c	NOUN
ap-9258	130	4	is	be	AUX
ap-9258	130	5	not	not	PART
ap-9258	130	6	located	locate	VERB
ap-9258	130	7	at	at	ADP
ap-9258	130	8	the	the	DET
ap-9258	130	9	exact	exact	ADJ
ap-9258	130	10	mid	mid	NOUN
ap-9258	130	11	-	-	NOUN
ap-9258	130	12	point	point	NOUN
ap-9258	130	13	,	,	PUNCT
ap-9258	130	14	hence	hence	ADV
ap-9258	130	15	the	the	DET
ap-9258	130	16	surface	surface	NOUN
ap-9258	130	17	is	be	AUX
ap-9258	130	18	non	non	ADJ
ap-9258	130	19	-	-	NOUN
ap-9258	130	20	symmetry	symmetry	NOUN
ap-9258	130	21	.	.	PUNCT
ap-9258	131	1	the	the	DET
ap-9258	131	2	total	total	ADJ
ap-9258	131	3	pressure	pressure	NOUN
ap-9258	131	4	integral	integral	ADJ
ap-9258	131	5	for	for	ADP
ap-9258	131	6	the	the	DET
ap-9258	131	7	triangular	triangular	NOUN
ap-9258	131	8	piston	piston	NOUN
ap-9258	131	9	takes	take	VERB
ap-9258	131	10	the	the	DET
ap-9258	131	11	form	form	NOUN
ap-9258	131	12	of	of	ADP
ap-9258	131	13	equation	equation	NOUN
ap-9258	131	14	(	(	PUNCT
ap-9258	131	15	16	16	NUM
ap-9258	131	16	)	)	PUNCT
ap-9258	131	17	.	.	PUNCT
ap-9258	132	1	the	the	DET
ap-9258	132	2	ab	ab	PROPN
ap-9258	132	3	of	of	ADP
ap-9258	132	4	the	the	DET
ap-9258	132	5	acoustic	acoustic	ADJ
ap-9258	132	6	element	element	NOUN
ap-9258	132	7	on	on	ADP
ap-9258	132	8	the	the	DET
ap-9258	132	9	surface	surface	NOUN
ap-9258	132	10	is	be	AUX
ap-9258	132	11	determined	determine	VERB
ap-9258	132	12	using	use	VERB
ap-9258	132	13	the	the	DET
ap-9258	132	14	principle	principle	NOUN
ap-9258	132	15	of	of	ADP
ap-9258	132	16	similar	similar	ADJ
ap-9258	132	17	triangles	triangle	NOUN
ap-9258	132	18	as	as	SCONJ
ap-9258	132	19	given	give	VERB
ap-9258	132	20	in	in	ADP
ap-9258	132	21	equation	equation	NOUN
ap-9258	132	22	(	(	PUNCT
ap-9258	132	23	17	17	NUM
ap-9258	132	24	)	)	PUNCT
ap-9258	132	25	.	.	PUNCT
ap-9258	133	1	substituting	substitute	VERB
ap-9258	133	2	r	r	NOUN
ap-9258	133	3	as	as	SCONJ
ap-9258	133	4	previously	previously	ADV
ap-9258	133	5	defined	define	VERB
ap-9258	133	6	in	in	ADP
ap-9258	133	7	equation	equation	NOUN
ap-9258	133	8	(	(	PUNCT
ap-9258	133	9	9	9	NUM
ap-9258	133	10	)	)	PUNCT
ap-9258	133	11	and	and	CCONJ
ap-9258	133	12	ds	ds	ADJ
ap-9258	133	13	=	=	ADJ
ap-9258	133	14	2(ab)dx	2(ab)dx	NOUN
ap-9258	133	15	while	while	SCONJ
ap-9258	133	16	retaining	retain	VERB
ap-9258	133	17	only	only	ADV
ap-9258	133	18	the	the	DET
ap-9258	133	19	real	real	ADJ
ap-9258	133	20	component	component	NOUN
ap-9258	133	21	of	of	ADP
ap-9258	133	22	the	the	DET
ap-9258	133	23	exponential	exponential	NOUN
ap-9258	133	24	as	as	ADP
ap-9258	133	25	previously	previously	ADV
ap-9258	133	26	done	do	VERB
ap-9258	133	27	in	in	ADP
ap-9258	133	28	the	the	DET
ap-9258	133	29	case	case	NOUN
ap-9258	133	30	of	of	ADP
ap-9258	133	31	the	the	DET
ap-9258	133	32	circular	circular	ADJ
ap-9258	133	33	piston	piston	NOUN
ap-9258	133	34	in	in	ADP
ap-9258	133	35	section	section	NOUN
ap-9258	133	36	3.1	3.1	NUM
ap-9258	133	37	,	,	PUNCT
ap-9258	133	38	equation	equation	NOUN
ap-9258	133	39	(	(	PUNCT
ap-9258	133	40	16	16	NUM
ap-9258	133	41	)	)	PUNCT
ap-9258	133	42	becomes	become	VERB
ap-9258	133	43	equation	equation	NOUN
ap-9258	133	44	(	(	PUNCT
ap-9258	133	45	18	18	NUM
ap-9258	133	46	)	)	PUNCT
ap-9258	133	47	.	.	PUNCT
ap-9258	134	1	then	then	ADV
ap-9258	134	2	,	,	PUNCT
ap-9258	134	3	the	the	DET
ap-9258	134	4	complex	complex	ADJ
ap-9258	134	5	component	component	NOUN
ap-9258	134	6	of	of	ADP
ap-9258	134	7	the	the	DET
ap-9258	134	8	pressure	pressure	NOUN
ap-9258	134	9	,	,	PUNCT
ap-9258	134	10	pt	pt	X
ap-9258	134	11	is	be	AUX
ap-9258	134	12	simplified	simplify	VERB
ap-9258	134	13	as	as	SCONJ
ap-9258	134	14	can	can	AUX
ap-9258	134	15	be	be	AUX
ap-9258	134	16	seen	see	VERB
ap-9258	134	17	from	from	ADP
ap-9258	134	18	equations	equation	NOUN
ap-9258	134	19	(	(	PUNCT
ap-9258	134	20	19)–(21	19)–(21	NUM
ap-9258	134	21	)	)	PUNCT
ap-9258	134	22	.	.	PUNCT
ap-9258	135	1	on	on	ADP
ap-9258	135	2	further	further	ADJ
ap-9258	135	3	manipulation	manipulation	NOUN
ap-9258	135	4	in	in	ADP
ap-9258	135	5	equation	equation	NOUN
ap-9258	135	6	(	(	PUNCT
ap-9258	135	7	22	22	NUM
ap-9258	135	8	)	)	PUNCT
ap-9258	135	9	,	,	PUNCT
ap-9258	135	10	pt	pt	PROPN
ap-9258	135	11	takes	take	VERB
ap-9258	135	12	the	the	DET
ap-9258	135	13	final	final	ADJ
ap-9258	135	14	form	form	NOUN
ap-9258	135	15	expressed	express	VERB
ap-9258	135	16	in	in	ADP
ap-9258	135	17	equation	equation	NOUN
ap-9258	135	18	(	(	PUNCT
ap-9258	135	19	23	23	NUM
ap-9258	135	20	)	)	PUNCT
ap-9258	135	21	from	from	ADP
ap-9258	135	22	which	which	PRON
ap-9258	135	23	the	the	DET
ap-9258	135	24	directional	directional	ADJ
ap-9258	135	25	factor	factor	NOUN
ap-9258	135	26	is	be	AUX
ap-9258	135	27	isolated	isolate	VERB
ap-9258	135	28	as	as	ADP
ap-9258	135	29	equation	equation	NOUN
ap-9258	135	30	(	(	PUNCT
ap-9258	135	31	24	24	NUM
ap-9258	135	32	)	)	PUNCT
ap-9258	135	33	.	.	PUNCT
ap-9258	136	1	pt	pt	X
ap-9258	137	1	=	=	SYM
ap-9258	137	2	i	i	PRON
ap-9258	137	3	∫	∫	PROPN
ap-9258	137	4	2√	2√	PROPN
ap-9258	137	5	3	3	NUM
ap-9258	137	6	at	at	ADP
ap-9258	137	7	−	−	PROPN
ap-9258	137	8	1√	1√	PROPN
ap-9258	137	9	3	3	NUM
ap-9258	137	10	at	at	ADP
ap-9258	137	11	a	a	DET
ap-9258	137	12	r	r	NOUN
ap-9258	137	13	ei(ωt−kr)ds	ei(ωt−kr)d	NOUN
ap-9258	137	14	,	,	PUNCT
ap-9258	137	15	(	(	PUNCT
ap-9258	137	16	16	16	NUM
ap-9258	137	17	)	)	PUNCT
ap-9258	137	18	ce	ce	PROPN
ap-9258	137	19	ce	ce	PROPN
ap-9258	138	1	+	+	CCONJ
ap-9258	138	2	x	x	X
ap-9258	138	3	=	=	SYM
ap-9258	138	4	cd	cd	PROPN
ap-9258	138	5	ab	ab	PROPN
ap-9258	138	6	=	=	SYM
ap-9258	138	7	ce	ce	PROPN
ap-9258	138	8	tan	tan	PROPN
ap-9258	138	9	30	30	NUM
ap-9258	138	10	ab	ab	PROPN
ap-9258	138	11	∴	∴	PROPN
ap-9258	138	12	ab	ab	PROPN
ap-9258	138	13	=	=	PUNCT
ap-9258	138	14	2	2	NUM
ap-9258	138	15	3at	3at	NOUN
ap-9258	139	1	+	+	CCONJ
ap-9258	139	2	1√	1√	PROPN
ap-9258	139	3	3	3	NUM
ap-9258	139	4	x	x	NOUN
ap-9258	139	5	,	,	PUNCT
ap-9258	139	6	(	(	PUNCT
ap-9258	139	7	17	17	NUM
ap-9258	139	8	)	)	PUNCT
ap-9258	139	9	pt	pt	NOUN
ap-9258	140	1	=	=	NOUN
ap-9258	140	2	i	i	PRON
ap-9258	140	3	a	a	DET
ap-9258	140	4	r	r	NOUN
ap-9258	140	5	ei(ωt−kr	ei(ωt−kr	NOUN
ap-9258	140	6	)	)	PUNCT
ap-9258	140	7	∫	∫	PROPN
ap-9258	141	1	2√	2√	PROPN
ap-9258	141	2	3	3	NUM
ap-9258	141	3	at	at	ADP
ap-9258	141	4	−	−	PROPN
ap-9258	141	5	1√	1√	PROPN
ap-9258	141	6	3	3	NUM
ap-9258	141	7	at	at	ADP
ap-9258	141	8	·	·	PUNCT
ap-9258	141	9	cos	cos	PROPN
ap-9258	141	10	(	(	PUNCT
ap-9258	141	11	kx	kx	PROPN
ap-9258	141	12	sin	sin	PROPN
ap-9258	141	13	θ	θ	PROPN
ap-9258	141	14	)	)	PUNCT
ap-9258	141	15	·	·	PUNCT
ap-9258	141	16	2	2	NUM
ap-9258	141	17	(	(	PUNCT
ap-9258	141	18	2	2	NUM
ap-9258	141	19	3at	3at	NOUN
ap-9258	141	20	+	+	CCONJ
ap-9258	141	21	1√	1√	ADJ
ap-9258	141	22	3	3	NUM
ap-9258	141	23	x	x	SYM
ap-9258	141	24	)	)	PUNCT
ap-9258	141	25	dx	dx	PROPN
ap-9258	141	26	,	,	PUNCT
ap-9258	141	27	(	(	PUNCT
ap-9258	141	28	18	18	NUM
ap-9258	141	29	)	)	PUNCT
ap-9258	141	30	=	=	NOUN
ap-9258	142	1	i	i	PRON
ap-9258	142	2	a	a	DET
ap-9258	142	3	r	r	NOUN
ap-9258	142	4	2ei(ωt−kr	2ei(ωt−kr	NOUN
ap-9258	142	5	)	)	PUNCT
ap-9258	142	6	{	{	PUNCT
ap-9258	142	7	2	2	NUM
ap-9258	142	8	3at	3at	NOUN
ap-9258	142	9	(	(	PUNCT
ap-9258	142	10	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	142	11	sin	sin	NOUN
ap-9258	142	12	(	(	PUNCT
ap-9258	142	13	kx	kx	PROPN
ap-9258	142	14	sin	sin	PROPN
ap-9258	142	15	θ	θ	PROPN
ap-9258	142	16	)	)	PUNCT
ap-9258	142	17	k	k	NOUN
ap-9258	142	18	sin	sin	NOUN
ap-9258	142	19	θ	θ	PROPN
ap-9258	142	20	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	142	21	2√	2√	PROPN
ap-9258	142	22	3	3	NUM
ap-9258	142	23	at	at	ADP
ap-9258	142	24	−	−	PROPN
ap-9258	142	25	1√	1√	PROPN
ap-9258	142	26	3	3	NUM
ap-9258	142	27	at	at	ADP
ap-9258	142	28	)	)	PUNCT
ap-9258	143	1	+	+	CCONJ
ap-9258	143	2	1√	1√	NUM
ap-9258	143	3	3	3	NUM
ap-9258	143	4	(	(	PUNCT
ap-9258	143	5	∣∣∣∣x	∣∣∣∣x	NOUN
ap-9258	143	6	sin	sin	NOUN
ap-9258	143	7	(	(	PUNCT
ap-9258	143	8	kx	kx	PROPN
ap-9258	143	9	sin	sin	PROPN
ap-9258	143	10	θ	θ	PROPN
ap-9258	143	11	)	)	PUNCT
ap-9258	143	12	k	k	NOUN
ap-9258	143	13	sin	sin	NOUN
ap-9258	143	14	θ	θ	PROPN
ap-9258	143	15	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	143	16	2√	2√	PROPN
ap-9258	143	17	3	3	NUM
ap-9258	143	18	at	at	ADP
ap-9258	143	19	−	−	PROPN
ap-9258	143	20	1√	1√	PROPN
ap-9258	143	21	3	3	NUM
ap-9258	143	22	at	at	ADP
ap-9258	143	23	)	)	PUNCT
ap-9258	144	1	+	+	CCONJ
ap-9258	144	2	1√	1√	NUM
ap-9258	144	3	3	3	NUM
ap-9258	144	4	(	(	PUNCT
ap-9258	144	5	∣∣∣∣cos	∣∣∣∣cos	PROPN
ap-9258	144	6	(	(	PUNCT
ap-9258	144	7	kx	kx	PROPN
ap-9258	144	8	sin	sin	PROPN
ap-9258	144	9	θ	θ	PROPN
ap-9258	144	10	)	)	PUNCT
ap-9258	144	11	k2	k2	ADJ
ap-9258	144	12	sin2	sin2	PROPN
ap-9258	144	13	θ	θ	PROPN
ap-9258	144	14	∣∣∣∣	∣∣∣∣	PROPN
ap-9258	144	15	2√	2√	PROPN
ap-9258	144	16	3	3	NUM
ap-9258	144	17	at	at	ADP
ap-9258	144	18	−	−	PROPN
ap-9258	144	19	1√	1√	PROPN
ap-9258	144	20	3	3	NUM
ap-9258	144	21	at	at	ADP
ap-9258	144	22	)	)	PUNCT
ap-9258	144	23	}	}	PUNCT
ap-9258	144	24	,	,	PUNCT
ap-9258	144	25	(	(	PUNCT
ap-9258	144	26	19	19	NUM
ap-9258	144	27	)	)	PUNCT
ap-9258	144	28	=	=	NOUN
ap-9258	145	1	i	i	PRON
ap-9258	145	2	a	a	DET
ap-9258	145	3	r	r	NOUN
ap-9258	145	4	2ei(ωt−kr	2ei(ωt−kr	NUM
ap-9258	145	5	)	)	PUNCT
ap-9258	145	6	2	2	NOUN
ap-9258	145	7	3at	3at	NOUN
ap-9258	145	8			PUNCT
ap-9258	145	9	sin	sin	NOUN
ap-9258	145	10	(	(	PUNCT
ap-9258	145	11	k	k	PROPN
ap-9258	145	12	2√	2√	PROPN
ap-9258	145	13	3	3	NUM
ap-9258	145	14	at	at	ADP
ap-9258	145	15	sin	sin	NOUN
ap-9258	145	16	θ	θ	PROPN
ap-9258	145	17	)	)	PUNCT
ap-9258	146	1	+	+	CCONJ
ap-9258	146	2	sin	sin	NOUN
ap-9258	146	3	(	(	PUNCT
ap-9258	146	4	k	k	PROPN
ap-9258	146	5	1√	1√	PROPN
ap-9258	146	6	3	3	NUM
ap-9258	146	7	at	at	ADP
ap-9258	146	8	sin	sin	NOUN
ap-9258	146	9	θ	θ	PROPN
ap-9258	146	10	)	)	PUNCT
ap-9258	147	1	k	k	PROPN
ap-9258	147	2	sin	sin	NOUN
ap-9258	147	3	θ	θ	X
ap-9258	147	4			NOUN
ap-9258	147	5	+	+	CCONJ
ap-9258	147	6			NUM
ap-9258	147	7	2	2	NUM
ap-9258	147	8	3	3	NUM
ap-9258	147	9	at	at	ADP
ap-9258	147	10	sin	sin	NOUN
ap-9258	147	11	(	(	PUNCT
ap-9258	147	12	k	k	PROPN
ap-9258	147	13	2√	2√	PROPN
ap-9258	147	14	3	3	NUM
ap-9258	147	15	at	at	ADP
ap-9258	147	16	sin	sin	NOUN
ap-9258	147	17	θ	θ	PROPN
ap-9258	147	18	)	)	PUNCT
ap-9258	148	1	−	−	ADP
ap-9258	148	2	1	1	NUM
ap-9258	148	3	3	3	NUM
ap-9258	148	4	at	at	ADP
ap-9258	148	5	sin	sin	NOUN
ap-9258	148	6	(	(	PUNCT
ap-9258	148	7	k	k	PROPN
ap-9258	148	8	1√	1√	PROPN
ap-9258	148	9	3	3	NUM
ap-9258	148	10	at	at	ADP
ap-9258	148	11	sin	sin	NOUN
ap-9258	148	12	θ	θ	PROPN
ap-9258	148	13	)	)	PUNCT
ap-9258	149	1	k	k	PROPN
ap-9258	149	2	sin	sin	PROPN
ap-9258	149	3	θ	θ	PROPN
ap-9258	149	4	+	+	AUX
ap-9258	149	5	1√	1√	PROPN
ap-9258	149	6	3	3	NUM
ap-9258	149	7	cos	co	NOUN
ap-9258	149	8	(	(	PUNCT
ap-9258	149	9	k	k	PROPN
ap-9258	149	10	2√	2√	PROPN
ap-9258	149	11	3	3	NUM
ap-9258	149	12	at	at	ADP
ap-9258	149	13	sin	sin	NOUN
ap-9258	149	14	θ	θ	PROPN
ap-9258	149	15	)	)	PUNCT
ap-9258	150	1	−	−	PROPN
ap-9258	151	1	cos	cos	INTJ
ap-9258	151	2	(	(	PUNCT
ap-9258	151	3	k	k	PROPN
ap-9258	151	4	1√	1√	PROPN
ap-9258	151	5	3	3	NUM
ap-9258	151	6	at	at	ADP
ap-9258	151	7	sin	sin	NOUN
ap-9258	151	8	θ	θ	PROPN
ap-9258	151	9	)	)	PUNCT
ap-9258	151	10	k2	k2	PROPN
ap-9258	151	11	sin2	sin2	NOUN
ap-9258	151	12	θ	θ	PROPN
ap-9258	152	1			NOUN
ap-9258	152	2			NOUN
ap-9258	152	3	,	,	PUNCT
ap-9258	152	4	(	(	PUNCT
ap-9258	152	5	20	20	NUM
ap-9258	152	6	)	)	PUNCT
ap-9258	152	7	pt	pt	NOUN
ap-9258	153	1	=	=	NOUN
ap-9258	153	2	i	i	PRON
ap-9258	153	3	a	a	DET
ap-9258	153	4	r	r	NOUN
ap-9258	153	5	2ei(ωt−kr	2ei(ωt−kr	PROPN
ap-9258	153	6	)	)	PUNCT
ap-9258	153	7	4	4	PROPN
ap-9258	153	8	3at	3at	ADJ
ap-9258	153	9			PUNCT
ap-9258	153	10	sin	sin	NOUN
ap-9258	153	11	(	(	PUNCT
ap-9258	153	12	k	k	PROPN
ap-9258	153	13	2√	2√	PROPN
ap-9258	153	14	3	3	NUM
ap-9258	153	15	at	at	ADP
ap-9258	153	16	sin	sin	NOUN
ap-9258	153	17	θ	θ	PROPN
ap-9258	153	18	)	)	PUNCT
ap-9258	154	1	k	k	PROPN
ap-9258	154	2	sin	sin	PROPN
ap-9258	154	3	θ	θ	PROPN
ap-9258	154	4	+	+	AUX
ap-9258	154	5	1	1	NUM
ap-9258	154	6	3at	3at	ADJ
ap-9258	154	7			PUNCT
ap-9258	154	8	sin	sin	NOUN
ap-9258	154	9	(	(	PUNCT
ap-9258	154	10	k	k	PROPN
ap-9258	154	11	1√	1√	PROPN
ap-9258	154	12	3	3	NUM
ap-9258	154	13	at	at	ADP
ap-9258	154	14	sin	sin	NOUN
ap-9258	154	15	θ	θ	PROPN
ap-9258	154	16	)	)	PUNCT
ap-9258	155	1	k	k	PROPN
ap-9258	155	2	sin	sin	VERB
ap-9258	155	3	θ	θ	PROPN
ap-9258	155	4			NOUN
ap-9258	155	5	−	−	PROPN
ap-9258	155	6	2√	2√	NUM
ap-9258	155	7	3	3	NUM
ap-9258	155	8			NOUN
ap-9258	155	9	sin	sin	NOUN
ap-9258	155	10	(	(	PUNCT
ap-9258	155	11	k	k	NOUN
ap-9258	155	12	√	√	ADJ
ap-9258	155	13	3	3	NUM
ap-9258	155	14	2	2	NUM
ap-9258	155	15	at	at	ADP
ap-9258	155	16	sin	sin	NOUN
ap-9258	155	17	θ	θ	PROPN
ap-9258	155	18	)	)	PUNCT
ap-9258	155	19	sin	sin	NOUN
ap-9258	155	20	(	(	PUNCT
ap-9258	155	21	k	k	NOUN
ap-9258	155	22	√	√	ADV
ap-9258	155	23	3	3	NUM
ap-9258	155	24	6	6	NUM
ap-9258	155	25	at	at	ADP
ap-9258	155	26	sin	sin	NOUN
ap-9258	155	27	θ	θ	PROPN
ap-9258	155	28	)	)	PUNCT
ap-9258	156	1	k2	k2	PROPN
ap-9258	156	2	sin2	sin2	NOUN
ap-9258	156	3	θ	θ	PROPN
ap-9258	156	4			NOUN
ap-9258	156	5			NOUN
ap-9258	156	6	,	,	PUNCT
ap-9258	156	7	(	(	PUNCT
ap-9258	156	8	21	21	NUM
ap-9258	156	9	)	)	PUNCT
ap-9258	156	10	474	474	NUM
ap-9258	156	11	vol	vol	NOUN
ap-9258	156	12	.	.	PROPN
ap-9258	157	1	64	64	NUM
ap-9258	157	2	no	no	NOUN
ap-9258	157	3	.	.	PUNCT
ap-9258	158	1	5/2024	5/2024	ADJ
ap-9258	158	2	acoustic	acoustic	ADJ
ap-9258	158	3	radiation	radiation	NOUN
ap-9258	158	4	beam	beam	NOUN
ap-9258	158	5	patterns	pattern	NOUN
ap-9258	158	6	of	of	ADP
ap-9258	158	7	different	different	ADJ
ap-9258	158	8	polygonal	polygonal	NOUN
ap-9258	158	9	.	.	PUNCT
ap-9258	158	10	.	.	PUNCT
ap-9258	158	11	.	.	PUNCT
ap-9258	159	1	y	y	NOUN
ap-9258	159	2	x	x	PUNCT
ap-9258	159	3	c	c	PROPN
ap-9258	159	4	a	a	DET
ap-9258	159	5	d	d	X
ap-9258	159	6	b	b	X
ap-9258	159	7	e	e	NOUN
ap-9258	159	8	at	at	ADP
ap-9258	159	9	60o	60o	NOUN
ap-9258	159	10	(	(	PUNCT
ap-9258	159	11	a	a	X
ap-9258	159	12	)	)	PUNCT
ap-9258	159	13	.	.	PUNCT
ap-9258	160	1	surface	surface	NOUN
ap-9258	160	2	analysis	analysis	NOUN
ap-9258	160	3	.	.	PUNCT
ap-9258	161	1	c	c	NOUN
ap-9258	161	2	a	a	DET
ap-9258	161	3	θ	θ	PROPN
ap-9258	161	4	q	q	X
ap-9258	161	5	p	p	NOUN
ap-9258	161	6	r	r	NOUN
ap-9258	161	7	r	r	NOUN
ap-9258	161	8	z	z	NOUN
ap-9258	161	9	(	(	PUNCT
ap-9258	161	10	b	b	NOUN
ap-9258	161	11	)	)	PUNCT
ap-9258	161	12	.	.	PUNCT
ap-9258	162	1	radiation	radiation	NOUN
ap-9258	162	2	analysis	analysis	NOUN
ap-9258	162	3	.	.	PUNCT
ap-9258	163	1	figure	figure	NOUN
ap-9258	163	2	5	5	NUM
ap-9258	163	3	.	.	PUNCT
ap-9258	164	1	the	the	DET
ap-9258	164	2	geometry	geometry	NOUN
ap-9258	164	3	for	for	ADP
ap-9258	164	4	the	the	DET
ap-9258	164	5	derivation	derivation	NOUN
ap-9258	164	6	of	of	ADP
ap-9258	164	7	the	the	DET
ap-9258	164	8	directional	directional	ADJ
ap-9258	164	9	factor	factor	NOUN
ap-9258	164	10	of	of	ADP
ap-9258	164	11	a	a	DET
ap-9258	164	12	triangular	triangular	ADJ
ap-9258	164	13	acoustic	acoustic	ADJ
ap-9258	164	14	piston	piston	NOUN
ap-9258	164	15	source	source	NOUN
ap-9258	164	16	.	.	PUNCT
ap-9258	165	1	=	=	PRON
ap-9258	166	1	i	i	PRON
ap-9258	166	2	a	a	DET
ap-9258	166	3	r	r	NOUN
ap-9258	166	4	2ei(ωt−kr	2ei(ωt−kr	NUM
ap-9258	166	5	)	)	PUNCT
ap-9258	166	6			NOUN
ap-9258	166	7	8	8	NUM
ap-9258	166	8	3	3	NUM
ap-9258	166	9	√	√	NUM
ap-9258	166	10	3	3	NUM
ap-9258	166	11	at	at	ADP
ap-9258	166	12	2	2	NUM
ap-9258	166	13			NOUN
ap-9258	166	14	sin	sin	NOUN
ap-9258	166	15	(	(	PUNCT
ap-9258	166	16	k	k	PROPN
ap-9258	166	17	2√	2√	PROPN
ap-9258	166	18	3	3	NUM
ap-9258	166	19	at	at	ADP
ap-9258	166	20	sin	sin	NOUN
ap-9258	166	21	θ	θ	PROPN
ap-9258	166	22	)	)	PUNCT
ap-9258	167	1	k	k	PROPN
ap-9258	167	2	2√	2√	PROPN
ap-9258	167	3	3	3	NUM
ap-9258	167	4	at	at	ADP
ap-9258	167	5	sin	sin	NOUN
ap-9258	167	6	θ	θ	PROPN
ap-9258	167	7	+	+	VERB
ap-9258	167	8	1	1	NUM
ap-9258	167	9	3	3	NUM
ap-9258	167	10	√	√	NUM
ap-9258	167	11	3	3	NUM
ap-9258	167	12	at	at	ADP
ap-9258	167	13	2	2	NUM
ap-9258	167	14			NOUN
ap-9258	167	15	sin	sin	NOUN
ap-9258	167	16	(	(	PUNCT
ap-9258	167	17	k	k	PROPN
ap-9258	167	18	1√	1√	PROPN
ap-9258	167	19	3	3	NUM
ap-9258	167	20	at	at	ADP
ap-9258	167	21	sin	sin	NOUN
ap-9258	167	22	θ	θ	PROPN
ap-9258	167	23	)	)	PUNCT
ap-9258	168	1	k	k	PROPN
ap-9258	168	2	1√	1√	PROPN
ap-9258	168	3	3	3	NUM
ap-9258	168	4	at	at	ADP
ap-9258	168	5	sin	sin	NOUN
ap-9258	168	6	θ	θ	PROPN
ap-9258	168	7			ADV
ap-9258	168	8	−	−	NUM
ap-9258	168	9	1	1	NUM
ap-9258	168	10	2	2	NUM
ap-9258	168	11	√	√	NUM
ap-9258	168	12	3	3	NUM
ap-9258	168	13	at	at	ADP
ap-9258	168	14	2	2	NUM
ap-9258	168	15			NOUN
ap-9258	168	16	sin	sin	NOUN
ap-9258	168	17	(	(	PUNCT
ap-9258	168	18	k	k	NOUN
ap-9258	168	19	√	√	ADJ
ap-9258	168	20	3	3	NUM
ap-9258	168	21	2	2	NUM
ap-9258	168	22	at	at	ADP
ap-9258	168	23	sin	sin	NOUN
ap-9258	168	24	θ	θ	PROPN
ap-9258	168	25	)	)	PUNCT
ap-9258	169	1	k	k	X
ap-9258	169	2	√	√	ADV
ap-9258	169	3	3	3	NUM
ap-9258	169	4	2	2	NUM
ap-9258	169	5	at	at	ADP
ap-9258	169	6	sin	sin	NOUN
ap-9258	169	7	θ	θ	PROPN
ap-9258	169	8	·	·	PUNCT
ap-9258	169	9	sin	sin	NOUN
ap-9258	169	10	(	(	PUNCT
ap-9258	169	11	k	k	NOUN
ap-9258	169	12	√	√	ADJ
ap-9258	169	13	3	3	NUM
ap-9258	169	14	6	6	NUM
ap-9258	169	15	at	at	ADP
ap-9258	169	16	sin	sin	NOUN
ap-9258	169	17	θ	θ	PROPN
ap-9258	169	18	)	)	PUNCT
ap-9258	170	1	k	k	X
ap-9258	170	2	√	√	ADV
ap-9258	170	3	3	3	NUM
ap-9258	170	4	6	6	NUM
ap-9258	170	5	at	at	ADP
ap-9258	170	6	sin	sin	NOUN
ap-9258	170	7	θ	θ	PROPN
ap-9258	170	8			NOUN
ap-9258	170	9			NOUN
ap-9258	170	10	,	,	PUNCT
ap-9258	170	11	(	(	PUNCT
ap-9258	170	12	22	22	NUM
ap-9258	170	13	)	)	PUNCT
ap-9258	170	14	pt	pt	NOUN
ap-9258	171	1	=	=	NOUN
ap-9258	171	2	i	i	PRON
ap-9258	171	3	a	a	DET
ap-9258	171	4	r	r	NOUN
ap-9258	171	5	16	16	NUM
ap-9258	171	6	3	3	NUM
ap-9258	171	7	√	√	NUM
ap-9258	171	8	3	3	NUM
ap-9258	171	9	at	at	ADP
ap-9258	171	10	2ei(ωt−kr	2ei(ωt−kr	NUM
ap-9258	171	11	)	)	PUNCT
ap-9258	171	12			NOUN
ap-9258	171	13	sin	sin	NOUN
ap-9258	171	14	(	(	PUNCT
ap-9258	171	15	k	k	PROPN
ap-9258	171	16	2√	2√	PROPN
ap-9258	171	17	3	3	NUM
ap-9258	171	18	at	at	ADP
ap-9258	171	19	sin	sin	NOUN
ap-9258	171	20	θ	θ	PROPN
ap-9258	171	21	)	)	PUNCT
ap-9258	172	1	k	k	PROPN
ap-9258	172	2	2√	2√	PROPN
ap-9258	172	3	3	3	NUM
ap-9258	172	4	at	at	ADP
ap-9258	172	5	sin	sin	NOUN
ap-9258	172	6	θ	θ	PROPN
ap-9258	172	7	+	+	CCONJ
ap-9258	172	8	1	1	NUM
ap-9258	172	9	8	8	NUM
ap-9258	172	10			NOUN
ap-9258	172	11	sin	sin	NOUN
ap-9258	172	12	(	(	PUNCT
ap-9258	172	13	k	k	PROPN
ap-9258	172	14	1√	1√	PROPN
ap-9258	172	15	3	3	NUM
ap-9258	172	16	at	at	ADP
ap-9258	172	17	sin	sin	NOUN
ap-9258	172	18	θ	θ	PROPN
ap-9258	172	19	)	)	PUNCT
ap-9258	173	1	k	k	PROPN
ap-9258	173	2	1√	1√	PROPN
ap-9258	173	3	3	3	NUM
ap-9258	173	4	at	at	ADP
ap-9258	173	5	sin	sin	NOUN
ap-9258	173	6	θ	θ	PROPN
ap-9258	174	1			NOUN
ap-9258	174	2	−	−	PROPN
ap-9258	174	3	3	3	NUM
ap-9258	174	4	16	16	NUM
ap-9258	174	5			NOUN
ap-9258	174	6	sin	sin	NOUN
ap-9258	174	7	(	(	PUNCT
ap-9258	174	8	k	k	NOUN
ap-9258	174	9	√	√	ADJ
ap-9258	174	10	3	3	NUM
ap-9258	174	11	2	2	NUM
ap-9258	174	12	at	at	ADP
ap-9258	174	13	sin	sin	NOUN
ap-9258	174	14	θ	θ	PROPN
ap-9258	174	15	)	)	PUNCT
ap-9258	175	1	k	k	X
ap-9258	175	2	√	√	ADV
ap-9258	175	3	3	3	NUM
ap-9258	175	4	2	2	NUM
ap-9258	175	5	at	at	ADP
ap-9258	175	6	sin	sin	NOUN
ap-9258	175	7	θ	θ	PROPN
ap-9258	175	8	·	·	PUNCT
ap-9258	175	9	sin	sin	NOUN
ap-9258	175	10	(	(	PUNCT
ap-9258	175	11	k	k	NOUN
ap-9258	175	12	√	√	ADJ
ap-9258	175	13	3	3	NUM
ap-9258	175	14	6	6	NUM
ap-9258	175	15	at	at	ADP
ap-9258	175	16	sin	sin	NOUN
ap-9258	175	17	θ	θ	PROPN
ap-9258	175	18	)	)	PUNCT
ap-9258	176	1	k	k	X
ap-9258	176	2	√	√	ADV
ap-9258	176	3	3	3	NUM
ap-9258	176	4	6	6	NUM
ap-9258	176	5	at	at	ADP
ap-9258	176	6	sin	sin	NOUN
ap-9258	176	7	θ	θ	PROPN
ap-9258	176	8			NOUN
ap-9258	176	9			NOUN
ap-9258	176	10	,	,	PUNCT
ap-9258	176	11	(	(	PUNCT
ap-9258	176	12	23	23	NUM
ap-9258	176	13	)	)	PUNCT
ap-9258	176	14	ht	ht	PROPN
ap-9258	176	15	=	=	PUNCT
ap-9258	176	16	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ap-9258	176	17	sin	sin	NOUN
ap-9258	176	18	(	(	PUNCT
ap-9258	176	19	k	k	PROPN
ap-9258	176	20	2√	2√	PROPN
ap-9258	176	21	3	3	NUM
ap-9258	176	22	at	at	ADP
ap-9258	176	23	sin	sin	NOUN
ap-9258	176	24	θ	θ	PROPN
ap-9258	176	25	)	)	PUNCT
ap-9258	177	1	k	k	PROPN
ap-9258	177	2	2√	2√	PROPN
ap-9258	177	3	3	3	NUM
ap-9258	177	4	at	at	ADP
ap-9258	177	5	sin	sin	NOUN
ap-9258	177	6	θ	θ	PROPN
ap-9258	177	7	+	+	CCONJ
ap-9258	177	8	1	1	NUM
ap-9258	177	9	8	8	NUM
ap-9258	177	10			NOUN
ap-9258	177	11	sin	sin	NOUN
ap-9258	177	12	(	(	PUNCT
ap-9258	177	13	k	k	PROPN
ap-9258	177	14	1√	1√	PROPN
ap-9258	177	15	3	3	NUM
ap-9258	177	16	at	at	ADP
ap-9258	177	17	sin	sin	NOUN
ap-9258	177	18	θ	θ	PROPN
ap-9258	177	19	)	)	PUNCT
ap-9258	178	1	k	k	PROPN
ap-9258	178	2	1√	1√	PROPN
ap-9258	178	3	3	3	NUM
ap-9258	178	4	at	at	ADP
ap-9258	178	5	sin	sin	NOUN
ap-9258	178	6	θ	θ	PROPN
ap-9258	178	7	−	−	PROPN
ap-9258	178	8	3	3	NUM
ap-9258	178	9	16	16	NUM
ap-9258	178	10			NOUN
ap-9258	178	11	sin	sin	NOUN
ap-9258	178	12	(	(	PUNCT
ap-9258	178	13	k	k	NOUN
ap-9258	178	14	√	√	ADJ
ap-9258	178	15	3	3	NUM
ap-9258	178	16	2	2	NUM
ap-9258	178	17	at	at	ADP
ap-9258	178	18	sin	sin	NOUN
ap-9258	178	19	θ	θ	PROPN
ap-9258	178	20	)	)	PUNCT
ap-9258	179	1	k	k	X
ap-9258	179	2	√	√	ADV
ap-9258	179	3	3	3	NUM
ap-9258	179	4	2	2	NUM
ap-9258	179	5	at	at	ADP
ap-9258	179	6	sin	sin	NOUN
ap-9258	179	7	θ	θ	PROPN
ap-9258	179	8	·	·	PUNCT
ap-9258	179	9	sin	sin	NOUN
ap-9258	179	10	(	(	PUNCT
ap-9258	179	11	k	k	NOUN
ap-9258	179	12	√	√	ADJ
ap-9258	179	13	3	3	NUM
ap-9258	179	14	6	6	NUM
ap-9258	179	15	at	at	ADP
ap-9258	179	16	sin	sin	NOUN
ap-9258	179	17	θ	θ	PROPN
ap-9258	179	18	)	)	PUNCT
ap-9258	180	1	k	k	X
ap-9258	180	2	√	√	ADV
ap-9258	180	3	3	3	NUM
ap-9258	180	4	6	6	NUM
ap-9258	180	5	at	at	ADP
ap-9258	180	6	sin	sin	NOUN
ap-9258	180	7	θ	θ	PROPN
ap-9258	180	8			PROPN
ap-9258	180	9	∣∣∣∣∣∣.	∣∣∣∣∣∣.	PROPN
ap-9258	180	10	(	(	PUNCT
ap-9258	180	11	24	24	NUM
ap-9258	180	12	)	)	PUNCT
ap-9258	180	13	3.3	3.3	NUM
ap-9258	180	14	.	.	PUNCT
ap-9258	181	1	rectangular	rectangular	ADJ
ap-9258	181	2	and	and	CCONJ
ap-9258	181	3	square	square	ADJ
ap-9258	181	4	pistons	piston	NOUN
ap-9258	181	5	the	the	DET
ap-9258	181	6	rectangle	rectangle	NOUN
ap-9258	181	7	and	and	CCONJ
ap-9258	181	8	the	the	DET
ap-9258	181	9	square	square	NOUN
ap-9258	181	10	have	have	VERB
ap-9258	181	11	identical	identical	ADJ
ap-9258	181	12	geometries	geometry	NOUN
ap-9258	181	13	except	except	SCONJ
ap-9258	181	14	that	that	SCONJ
ap-9258	181	15	the	the	DET
ap-9258	181	16	latter	latter	NOUN
ap-9258	181	17	is	be	AUX
ap-9258	181	18	regular	regular	ADJ
ap-9258	181	19	by	by	ADP
ap-9258	181	20	having	have	VERB
ap-9258	181	21	equal	equal	ADJ
ap-9258	181	22	sides	side	NOUN
ap-9258	181	23	.	.	PUNCT
ap-9258	182	1	consequently	consequently	ADV
ap-9258	182	2	,	,	PUNCT
ap-9258	182	3	the	the	DET
ap-9258	182	4	directional	directional	ADJ
ap-9258	182	5	factor	factor	NOUN
ap-9258	182	6	when	when	SCONJ
ap-9258	182	7	successfully	successfully	ADV
ap-9258	182	8	derived	derive	VERB
ap-9258	182	9	for	for	ADP
ap-9258	182	10	one	one	NUM
ap-9258	182	11	can	can	AUX
ap-9258	182	12	be	be	AUX
ap-9258	182	13	used	use	VERB
ap-9258	182	14	to	to	PART
ap-9258	182	15	predict	predict	VERB
ap-9258	182	16	the	the	DET
ap-9258	182	17	other	other	ADJ
ap-9258	182	18	without	without	ADP
ap-9258	182	19	the	the	DET
ap-9258	182	20	repetition	repetition	NOUN
ap-9258	182	21	of	of	ADP
ap-9258	182	22	the	the	DET
ap-9258	182	23	procedures	procedure	NOUN
ap-9258	182	24	.	.	PUNCT
ap-9258	183	1	the	the	DET
ap-9258	183	2	acoustic	acoustic	ADJ
ap-9258	183	3	element	element	NOUN
ap-9258	183	4	lying	lie	VERB
ap-9258	183	5	parallel	parallel	NOUN
ap-9258	183	6	to	to	ADP
ap-9258	183	7	the	the	DET
ap-9258	183	8	y	y	PROPN
ap-9258	183	9	-axis	-axis	NOUN
ap-9258	183	10	on	on	ADP
ap-9258	183	11	the	the	DET
ap-9258	183	12	surface	surface	NOUN
ap-9258	183	13	of	of	ADP
ap-9258	183	14	the	the	DET
ap-9258	183	15	rectangular	rectangular	ADJ
ap-9258	183	16	surface	surface	NOUN
ap-9258	183	17	is	be	AUX
ap-9258	183	18	shown	show	VERB
ap-9258	183	19	in	in	ADP
ap-9258	183	20	figure	figure	NOUN
ap-9258	183	21	6	6	NUM
ap-9258	183	22	.	.	PUNCT
ap-9258	184	1	the	the	DET
ap-9258	184	2	surface	surface	NOUN
ap-9258	184	3	is	be	AUX
ap-9258	184	4	symmetrical	symmetrical	ADJ
ap-9258	184	5	since	since	SCONJ
ap-9258	184	6	the	the	DET
ap-9258	184	7	centre	centre	NOUN
ap-9258	184	8	c	c	PROPN
ap-9258	184	9	is	be	AUX
ap-9258	184	10	located	locate	VERB
ap-9258	184	11	at	at	ADP
ap-9258	184	12	the	the	DET
ap-9258	184	13	exact	exact	ADJ
ap-9258	184	14	midpoint	midpoint	NOUN
ap-9258	184	15	.	.	PUNCT
ap-9258	185	1	since	since	SCONJ
ap-9258	185	2	ab	ab	PROPN
ap-9258	185	3	=	=	PUNCT
ap-9258	185	4	ac	ac	PROPN
ap-9258	185	5	and	and	CCONJ
ap-9258	185	6	ds	ds	ADJ
ap-9258	185	7	=	=	SYM
ap-9258	185	8	2	2	NUM
ap-9258	185	9	ac	ac	PROPN
ap-9258	185	10	dx	dx	PROPN
ap-9258	185	11	,	,	PUNCT
ap-9258	185	12	the	the	DET
ap-9258	185	13	complex	complex	ADJ
ap-9258	185	14	pressure	pressure	NOUN
ap-9258	185	15	component	component	NOUN
ap-9258	185	16	pr	pr	NOUN
ap-9258	185	17	can	can	AUX
ap-9258	185	18	then	then	ADV
ap-9258	185	19	be	be	AUX
ap-9258	185	20	expressed	express	VERB
ap-9258	185	21	as	as	ADP
ap-9258	185	22	equation	equation	NOUN
ap-9258	185	23	(	(	PUNCT
ap-9258	185	24	25	25	NUM
ap-9258	185	25	)	)	PUNCT
ap-9258	185	26	.	.	PUNCT
ap-9258	186	1	this	this	DET
ap-9258	186	2	equation	equation	NOUN
ap-9258	186	3	is	be	AUX
ap-9258	186	4	simplified	simplify	VERB
ap-9258	186	5	from	from	ADP
ap-9258	186	6	equations	equation	NOUN
ap-9258	186	7	(	(	PUNCT
ap-9258	186	8	26)–(29	26)–(29	NUM
ap-9258	186	9	)	)	PUNCT
ap-9258	186	10	and	and	CCONJ
ap-9258	186	11	the	the	DET
ap-9258	186	12	directional	directional	ADJ
ap-9258	186	13	factor	factor	NOUN
ap-9258	186	14	of	of	ADP
ap-9258	186	15	the	the	DET
ap-9258	186	16	rectangular	rectangular	ADJ
ap-9258	186	17	surface	surface	NOUN
ap-9258	186	18	hr	hr	NOUN
ap-9258	186	19	is	be	AUX
ap-9258	186	20	then	then	ADV
ap-9258	186	21	isolated	isolate	VERB
ap-9258	186	22	as	as	SCONJ
ap-9258	186	23	given	give	VERB
ap-9258	186	24	in	in	ADP
ap-9258	186	25	equation	equation	NOUN
ap-9258	186	26	(	(	PUNCT
ap-9258	186	27	30	30	NUM
ap-9258	186	28	)	)	PUNCT
ap-9258	186	29	.	.	PUNCT
ap-9258	187	1	therefore	therefore	ADV
ap-9258	187	2	,	,	PUNCT
ap-9258	187	3	the	the	DET
ap-9258	187	4	directional	directional	ADJ
ap-9258	187	5	factor	factor	NOUN
ap-9258	187	6	of	of	ADP
ap-9258	187	7	the	the	DET
ap-9258	187	8	square	square	PROPN
ap-9258	187	9	piston	piston	NOUN
ap-9258	187	10	hs	hs	PROPN
ap-9258	187	11	takes	take	VERB
ap-9258	187	12	the	the	DET
ap-9258	187	13	form	form	NOUN
ap-9258	187	14	of	of	ADP
ap-9258	187	15	equation	equation	NOUN
ap-9258	187	16	(	(	PUNCT
ap-9258	187	17	31	31	NUM
ap-9258	187	18	)	)	PUNCT
ap-9258	187	19	.	.	PUNCT
ap-9258	188	1	pr	pr	NOUN
ap-9258	189	1	=	=	PUNCT
ap-9258	189	2	i	i	PRON
ap-9258	189	3	a	a	DET
ap-9258	189	4	r	r	NOUN
ap-9258	189	5	ei(ωt−kr	ei(ωt−kr	NOUN
ap-9258	189	6	)	)	PUNCT
ap-9258	189	7	∫	∫	PROPN
ap-9258	189	8	ar	ar	PROPN
ap-9258	189	9	−ar	−ar	PROPN
ap-9258	189	10	cos	cos	PROPN
ap-9258	189	11	(	(	PUNCT
ap-9258	189	12	kx	kx	PROPN
ap-9258	189	13	sin	sin	PROPN
ap-9258	189	14	θ)2acdx	θ)2acdx	NOUN
ap-9258	189	15	,	,	PUNCT
ap-9258	189	16	(	(	PUNCT
ap-9258	189	17	25	25	NUM
ap-9258	189	18	)	)	PUNCT
ap-9258	190	1	=	=	NOUN
ap-9258	191	1	i	i	PRON
ap-9258	191	2	a	a	DET
ap-9258	191	3	r	r	NOUN
ap-9258	191	4	ei(ωt−kr)2ac	ei(ωt−kr)2ac	NOUN
ap-9258	191	5	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	191	6	sin	sin	NOUN
ap-9258	191	7	(	(	PUNCT
ap-9258	191	8	kx	kx	PROPN
ap-9258	191	9	sin	sin	PROPN
ap-9258	191	10	θ	θ	PROPN
ap-9258	191	11	)	)	PUNCT
ap-9258	191	12	k	k	NOUN
ap-9258	191	13	sin	sin	NOUN
ap-9258	191	14	θ	θ	PROPN
ap-9258	191	15	∣∣∣∣	∣∣∣∣	PROPN
ap-9258	191	16	ar	ar	PROPN
ap-9258	191	17	−ar	−ar	PROPN
ap-9258	191	18	,	,	PUNCT
ap-9258	191	19	(	(	PUNCT
ap-9258	191	20	26	26	NUM
ap-9258	191	21	)	)	PUNCT
ap-9258	191	22	=	=	NOUN
ap-9258	192	1	i	i	PRON
ap-9258	192	2	a	a	DET
ap-9258	192	3	r	r	NOUN
ap-9258	192	4	ei(ωt−kr)2ac	ei(ωt−kr)2ac	X
ap-9258	192	5	(	(	PUNCT
ap-9258	192	6	sin	sin	NOUN
ap-9258	192	7	(	(	PUNCT
ap-9258	192	8	kar	kar	INTJ
ap-9258	192	9	sin	sin	PROPN
ap-9258	192	10	θ	θ	PROPN
ap-9258	192	11	)	)	PUNCT
ap-9258	192	12	+	+	CCONJ
ap-9258	192	13	sin	sin	NOUN
ap-9258	192	14	(	(	PUNCT
ap-9258	192	15	kar	kar	INTJ
ap-9258	192	16	sin	sin	PROPN
ap-9258	192	17	θ	θ	PROPN
ap-9258	192	18	)	)	PUNCT
ap-9258	192	19	k	k	PROPN
ap-9258	192	20	sin	sin	PROPN
ap-9258	192	21	θ	θ	PROPN
ap-9258	192	22	)	)	PUNCT
ap-9258	192	23	,	,	PUNCT
ap-9258	192	24	(	(	PUNCT
ap-9258	192	25	27	27	NUM
ap-9258	192	26	)	)	PUNCT
ap-9258	193	1	=	=	NOUN
ap-9258	194	1	i	i	PRON
ap-9258	194	2	a	a	DET
ap-9258	194	3	r	r	NOUN
ap-9258	194	4	ei(ωt−kr)4ac	ei(ωt−kr)4ac	NOUN
ap-9258	194	5	sin	sin	NOUN
ap-9258	194	6	(	(	PUNCT
ap-9258	194	7	kar	kar	INTJ
ap-9258	194	8	sin	sin	PROPN
ap-9258	194	9	θ	θ	PROPN
ap-9258	194	10	)	)	PUNCT
ap-9258	194	11	k	k	PROPN
ap-9258	194	12	sin	sin	PROPN
ap-9258	194	13	θ	θ	PROPN
ap-9258	194	14	,	,	PUNCT
ap-9258	194	15	(	(	PUNCT
ap-9258	194	16	28	28	NUM
ap-9258	194	17	)	)	PUNCT
ap-9258	194	18	475	475	NUM
ap-9258	194	19	t.	t.	NOUN
ap-9258	194	20	a.	a.	NOUN
ap-9258	194	21	yusuf	yusuf	PROPN
ap-9258	194	22	,	,	PUNCT
ap-9258	194	23	s.	s.	PROPN
ap-9258	194	24	a.	a.	PROPN
ap-9258	194	25	aodu	aodu	PROPN
ap-9258	194	26	,	,	PUNCT
ap-9258	194	27	a.	a.	NOUN
ap-9258	194	28	o.	o.	NOUN
ap-9258	194	29	alabi	alabi	PROPN
ap-9258	194	30	acta	acta	PROPN
ap-9258	194	31	polytechnica	polytechnica	PROPN
ap-9258	194	32	y	y	PROPN
ap-9258	194	33	x	x	PROPN
ap-9258	195	1	c	c	PROPN
ap-9258	195	2	a	a	DET
ap-9258	195	3	b	b	NOUN
ap-9258	195	4	ac	ac	ADP
ap-9258	195	5	45o	45o	PROPN
ap-9258	195	6	(	(	PUNCT
ap-9258	195	7	a	a	X
ap-9258	195	8	)	)	PUNCT
ap-9258	195	9	.	.	PUNCT
ap-9258	196	1	surface	surface	NOUN
ap-9258	196	2	analysis	analysis	NOUN
ap-9258	196	3	.	.	PUNCT
ap-9258	197	1	c	c	NOUN
ap-9258	197	2	a	a	DET
ap-9258	197	3	θ	θ	PROPN
ap-9258	197	4	q	q	X
ap-9258	198	1	p	p	NOUN
ap-9258	198	2	r	r	NOUN
ap-9258	198	3	r	r	NOUN
ap-9258	198	4	z	z	NOUN
ap-9258	198	5	θ	θ	NOUN
ap-9258	198	6	x	x	SYM
ap-9258	198	7	(	(	PUNCT
ap-9258	198	8	b	b	NOUN
ap-9258	198	9	)	)	PUNCT
ap-9258	198	10	.	.	PUNCT
ap-9258	199	1	radiation	radiation	NOUN
ap-9258	199	2	analysis	analysis	NOUN
ap-9258	199	3	.	.	PUNCT
ap-9258	200	1	figure	figure	NOUN
ap-9258	200	2	6	6	NUM
ap-9258	200	3	.	.	PUNCT
ap-9258	201	1	the	the	DET
ap-9258	201	2	geometry	geometry	NOUN
ap-9258	201	3	for	for	ADP
ap-9258	201	4	the	the	DET
ap-9258	201	5	derivation	derivation	NOUN
ap-9258	201	6	of	of	ADP
ap-9258	201	7	the	the	DET
ap-9258	201	8	directional	directional	ADJ
ap-9258	201	9	factor	factor	NOUN
ap-9258	201	10	of	of	ADP
ap-9258	201	11	a	a	DET
ap-9258	201	12	rectangular	rectangular	ADJ
ap-9258	201	13	acoustic	acoustic	ADJ
ap-9258	201	14	piston	piston	NOUN
ap-9258	201	15	source	source	NOUN
ap-9258	201	16	.	.	PUNCT
ap-9258	202	1	pr	pr	NOUN
ap-9258	203	1	=	=	PUNCT
ap-9258	203	2	i	i	PRON
ap-9258	203	3	a	a	DET
ap-9258	203	4	r	r	NOUN
ap-9258	203	5	ei(ωt−kr)4acar	ei(ωt−kr)4acar	NOUN
ap-9258	203	6	sin	sin	NOUN
ap-9258	203	7	(	(	PUNCT
ap-9258	203	8	kar	kar	INTJ
ap-9258	203	9	sin	sin	PROPN
ap-9258	203	10	θ	θ	PROPN
ap-9258	203	11	)	)	PUNCT
ap-9258	203	12	kar	kar	NOUN
ap-9258	203	13	sin	sin	PROPN
ap-9258	203	14	θ	θ	PROPN
ap-9258	203	15	,	,	PUNCT
ap-9258	203	16	(	(	PUNCT
ap-9258	203	17	29	29	NUM
ap-9258	203	18	)	)	PUNCT
ap-9258	203	19	hr	hr	NOUN
ap-9258	203	20	=	=	PUNCT
ap-9258	203	21	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	203	22	sin	sin	NOUN
ap-9258	203	23	(	(	PUNCT
ap-9258	203	24	kar	kar	INTJ
ap-9258	203	25	sin	sin	PROPN
ap-9258	203	26	θ	θ	PROPN
ap-9258	203	27	)	)	PUNCT
ap-9258	203	28	kar	kar	NOUN
ap-9258	203	29	sin	sin	NOUN
ap-9258	203	30	θ	θ	PROPN
ap-9258	203	31	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	203	32	=	=	PUNCT
ap-9258	203	33	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	203	34	sin	sin	NOUN
ap-9258	203	35	(	(	PUNCT
ap-9258	203	36	kar	kar	PROPN
ap-9258	203	37	tan	tan	PROPN
ap-9258	203	38	45	45	NUM
ap-9258	203	39	sin	sin	NOUN
ap-9258	203	40	θ	θ	PROPN
ap-9258	203	41	)	)	PUNCT
ap-9258	203	42	kar	kar	PROPN
ap-9258	203	43	tan	tan	PROPN
ap-9258	203	44	45	45	NUM
ap-9258	203	45	sin	sin	NOUN
ap-9258	203	46	θ	θ	PROPN
ap-9258	203	47	∣∣∣∣	∣∣∣∣	PROPN
ap-9258	203	48	,	,	PUNCT
ap-9258	203	49	(	(	PUNCT
ap-9258	203	50	30	30	NUM
ap-9258	203	51	)	)	PUNCT
ap-9258	203	52	hs	hs	PROPN
ap-9258	204	1	=	=	NOUN
ap-9258	204	2	∣∣∣∣	∣∣∣∣	PROPN
ap-9258	204	3	sin	sin	NOUN
ap-9258	204	4	(	(	PUNCT
ap-9258	204	5	kas	kas	X
ap-9258	204	6	sin	sin	PROPN
ap-9258	204	7	θ	θ	PROPN
ap-9258	204	8	)	)	PUNCT
ap-9258	204	9	kas	kas	PROPN
ap-9258	204	10	sin	sin	PROPN
ap-9258	204	11	θ	θ	PROPN
ap-9258	204	12	∣∣∣∣	∣∣∣∣	PROPN
ap-9258	204	13	=	=	PUNCT
ap-9258	204	14	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	204	15	sin	sin	NOUN
ap-9258	204	16	(	(	PUNCT
ap-9258	204	17	kas	kas	PROPN
ap-9258	204	18	tan	tan	PROPN
ap-9258	204	19	45	45	NUM
ap-9258	204	20	sin	sin	NOUN
ap-9258	204	21	θ	θ	PROPN
ap-9258	204	22	)	)	PUNCT
ap-9258	204	23	kas	kas	PROPN
ap-9258	204	24	tan	tan	PROPN
ap-9258	204	25	45	45	NUM
ap-9258	204	26	sin	sin	NOUN
ap-9258	204	27	θ	θ	PROPN
ap-9258	204	28	∣∣∣∣.	∣∣∣∣.	PROPN
ap-9258	204	29	(	(	PUNCT
ap-9258	204	30	31	31	NUM
ap-9258	204	31	)	)	PUNCT
ap-9258	204	32	3.4	3.4	NUM
ap-9258	204	33	.	.	PUNCT
ap-9258	205	1	pentagonal	pentagonal	ADJ
ap-9258	205	2	piston	piston	NOUN
ap-9258	205	3	figure	figure	NOUN
ap-9258	205	4	7	7	NUM
ap-9258	205	5	shows	show	VERB
ap-9258	205	6	the	the	DET
ap-9258	205	7	location	location	NOUN
ap-9258	205	8	of	of	ADP
ap-9258	205	9	the	the	DET
ap-9258	205	10	centre	centre	NOUN
ap-9258	205	11	c	c	PROPN
ap-9258	205	12	with	with	ADP
ap-9258	205	13	respect	respect	NOUN
ap-9258	205	14	to	to	ADP
ap-9258	205	15	the	the	DET
ap-9258	205	16	top	top	NOUN
ap-9258	205	17	and	and	CCONJ
ap-9258	205	18	bottom	bottom	NOUN
ap-9258	205	19	of	of	ADP
ap-9258	205	20	the	the	DET
ap-9258	205	21	radiation	radiation	NOUN
ap-9258	205	22	surface	surface	NOUN
ap-9258	205	23	of	of	ADP
ap-9258	205	24	a	a	DET
ap-9258	205	25	regular	regular	ADJ
ap-9258	205	26	pentagon	pentagon	NOUN
ap-9258	205	27	.	.	PUNCT
ap-9258	206	1	just	just	ADV
ap-9258	206	2	like	like	ADP
ap-9258	206	3	the	the	DET
ap-9258	206	4	triangle	triangle	NOUN
ap-9258	206	5	,	,	PUNCT
ap-9258	206	6	the	the	DET
ap-9258	206	7	surface	surface	NOUN
ap-9258	206	8	is	be	AUX
ap-9258	206	9	non	non	ADJ
ap-9258	206	10	-	-	ADJ
ap-9258	206	11	symmetrical	symmetrical	ADJ
ap-9258	206	12	since	since	SCONJ
ap-9258	206	13	the	the	DET
ap-9258	206	14	point	point	NOUN
ap-9258	206	15	c	c	NOUN
ap-9258	206	16	is	be	AUX
ap-9258	206	17	not	not	PART
ap-9258	206	18	located	locate	VERB
ap-9258	206	19	at	at	ADP
ap-9258	206	20	the	the	DET
ap-9258	206	21	exact	exact	ADJ
ap-9258	206	22	midpoint	midpoint	NOUN
ap-9258	206	23	of	of	ADP
ap-9258	206	24	the	the	DET
ap-9258	206	25	surface	surface	NOUN
ap-9258	206	26	.	.	PUNCT
ap-9258	207	1	the	the	DET
ap-9258	207	2	height	height	NOUN
ap-9258	207	3	of	of	ADP
ap-9258	207	4	the	the	DET
ap-9258	207	5	extruded	extruded	ADJ
ap-9258	207	6	triangle	triangle	NOUN
ap-9258	207	7	as	as	SCONJ
ap-9258	207	8	given	give	VERB
ap-9258	207	9	in	in	ADP
ap-9258	207	10	the	the	DET
ap-9258	207	11	figure	figure	NOUN
ap-9258	207	12	allows	allow	VERB
ap-9258	207	13	us	we	PRON
ap-9258	207	14	to	to	PART
ap-9258	207	15	find	find	VERB
ap-9258	207	16	the	the	DET
ap-9258	207	17	hsl	hsl	NOUN
ap-9258	207	18	,	,	PUNCT
ap-9258	207	19	ab	ab	PROPN
ap-9258	207	20	of	of	ADP
ap-9258	207	21	the	the	DET
ap-9258	207	22	acoustic	acoustic	ADJ
ap-9258	207	23	element	element	NOUN
ap-9258	207	24	on	on	ADP
ap-9258	207	25	that	that	DET
ap-9258	207	26	surface	surface	NOUN
ap-9258	207	27	by	by	ADP
ap-9258	207	28	the	the	DET
ap-9258	207	29	principle	principle	NOUN
ap-9258	207	30	of	of	ADP
ap-9258	207	31	similar	similar	ADJ
ap-9258	207	32	triangles	triangle	NOUN
ap-9258	207	33	as	as	SCONJ
ap-9258	207	34	given	give	VERB
ap-9258	207	35	in	in	ADP
ap-9258	207	36	equation	equation	NOUN
ap-9258	207	37	(	(	PUNCT
ap-9258	207	38	32	32	NUM
ap-9258	207	39	)	)	PUNCT
ap-9258	207	40	.	.	PUNCT
ap-9258	208	1	consequently	consequently	ADV
ap-9258	208	2	,	,	PUNCT
ap-9258	208	3	the	the	DET
ap-9258	208	4	integral	integral	ADJ
ap-9258	208	5	for	for	ADP
ap-9258	208	6	calculating	calculate	VERB
ap-9258	208	7	the	the	DET
ap-9258	208	8	complex	complex	ADJ
ap-9258	208	9	component	component	NOUN
ap-9258	208	10	of	of	ADP
ap-9258	208	11	the	the	DET
ap-9258	208	12	pressure	pressure	NOUN
ap-9258	208	13	pp	pp	ADV
ap-9258	208	14	is	be	AUX
ap-9258	208	15	given	give	VERB
ap-9258	208	16	in	in	ADP
ap-9258	208	17	equation	equation	NOUN
ap-9258	208	18	(	(	PUNCT
ap-9258	208	19	33	33	NUM
ap-9258	208	20	)	)	PUNCT
ap-9258	208	21	and	and	CCONJ
ap-9258	208	22	simplified	simplify	VERB
ap-9258	208	23	through	through	ADP
ap-9258	208	24	equations	equation	NOUN
ap-9258	208	25	(	(	PUNCT
ap-9258	208	26	34)–(36	34)–(36	NUM
ap-9258	208	27	)	)	PUNCT
ap-9258	208	28	.	.	PUNCT
ap-9258	209	1	when	when	SCONJ
ap-9258	209	2	further	far	ADV
ap-9258	209	3	manipulated	manipulate	VERB
ap-9258	209	4	mathematically	mathematically	ADV
ap-9258	209	5	,	,	PUNCT
ap-9258	209	6	equation	equation	NOUN
ap-9258	209	7	(	(	PUNCT
ap-9258	209	8	36	36	NUM
ap-9258	209	9	)	)	PUNCT
ap-9258	209	10	can	can	AUX
ap-9258	209	11	be	be	AUX
ap-9258	209	12	expressed	express	VERB
ap-9258	209	13	as	as	ADP
ap-9258	209	14	given	give	VERB
ap-9258	209	15	in	in	ADP
ap-9258	209	16	equation	equation	NOUN
ap-9258	209	17	(	(	PUNCT
ap-9258	209	18	37	37	NUM
ap-9258	209	19	)	)	PUNCT
ap-9258	209	20	.	.	PUNCT
ap-9258	210	1	from	from	ADP
ap-9258	210	2	this	this	DET
ap-9258	210	3	equation	equation	NOUN
ap-9258	210	4	,	,	PUNCT
ap-9258	210	5	the	the	DET
ap-9258	210	6	directional	directional	ADJ
ap-9258	210	7	factor	factor	NOUN
ap-9258	210	8	for	for	ADP
ap-9258	210	9	the	the	DET
ap-9258	210	10	pentagon	pentagon	PROPN
ap-9258	210	11	surface	surface	NOUN
ap-9258	210	12	hp	hp	PROPN
ap-9258	210	13	can	can	AUX
ap-9258	210	14	be	be	AUX
ap-9258	210	15	isolated	isolate	VERB
ap-9258	210	16	as	as	SCONJ
ap-9258	210	17	given	give	VERB
ap-9258	210	18	in	in	ADP
ap-9258	210	19	equation	equation	NOUN
ap-9258	210	20	(	(	PUNCT
ap-9258	210	21	38	38	NUM
ap-9258	210	22	)	)	PUNCT
ap-9258	210	23	,	,	PUNCT
ap-9258	210	24	applying	apply	VERB
ap-9258	210	25	trigonometry	trigonometry	NOUN
ap-9258	210	26	identity	identity	NOUN
ap-9258	210	27	,	,	PUNCT
ap-9258	210	28	this	this	DET
ap-9258	210	29	equation	equation	NOUN
ap-9258	210	30	is	be	AUX
ap-9258	210	31	further	far	ADV
ap-9258	210	32	worked	work	VERB
ap-9258	210	33	down	down	ADP
ap-9258	210	34	through	through	ADP
ap-9258	210	35	equations	equation	NOUN
ap-9258	210	36	(	(	PUNCT
ap-9258	210	37	39)–(40	39)–(40	NUM
ap-9258	210	38	)	)	PUNCT
ap-9258	210	39	.	.	PUNCT
ap-9258	211	1	ap	ap	PROPN
ap-9258	211	2	tan	tan	PROPN
ap-9258	211	3	72	72	NUM
ap-9258	212	1	ap	ap	NOUN
ap-9258	212	2	tan	tan	PROPN
ap-9258	212	3	72	72	NUM
ap-9258	213	1	+	+	CCONJ
ap-9258	213	2	(	(	PUNCT
ap-9258	213	3	ap	ap	PROPN
ap-9258	213	4	tan	tan	PROPN
ap-9258	213	5	54	54	NUM
ap-9258	213	6	−	−	NOUN
ap-9258	213	7	x	x	NOUN
ap-9258	213	8	)	)	PUNCT
ap-9258	213	9	=	=	SYM
ap-9258	213	10	ap	ap	PROPN
ap-9258	213	11	ab	ab	PROPN
ap-9258	213	12	∴	∴	PROPN
ap-9258	213	13	ab	ab	PROPN
ap-9258	214	1	=	=	PUNCT
ap-9258	214	2	(	(	PUNCT
ap-9258	214	3	1	1	NUM
ap-9258	214	4	+	+	NUM
ap-9258	214	5	tan	tan	PROPN
ap-9258	214	6	54	54	NUM
ap-9258	214	7	tan	tan	NOUN
ap-9258	214	8	18	18	NUM
ap-9258	214	9	)	)	PUNCT
ap-9258	214	10	ap	ap	NOUN
ap-9258	215	1	−	−	PROPN
ap-9258	216	1	x	x	SYM
ap-9258	216	2	tan	tan	PROPN
ap-9258	216	3	18	18	NUM
ap-9258	216	4	,	,	PUNCT
ap-9258	216	5	(	(	PUNCT
ap-9258	216	6	32	32	NUM
ap-9258	216	7	)	)	PUNCT
ap-9258	216	8	pp	pp	ADP
ap-9258	217	1	=	=	PUNCT
ap-9258	217	2	i	i	PRON
ap-9258	217	3	a	a	DET
ap-9258	217	4	r	r	NOUN
ap-9258	217	5	ei(ωt−kr	ei(ωt−kr	NOUN
ap-9258	217	6	)	)	PUNCT
ap-9258	217	7	∫	∫	PROPN
ap-9258	217	8	1	1	NUM
ap-9258	217	9	cos	cos	PROPN
ap-9258	217	10	54	54	NUM
ap-9258	217	11	a	a	DET
ap-9258	217	12	p	p	PRON
ap-9258	217	13	−ap	−ap	PROPN
ap-9258	217	14	tan	tan	PROPN
ap-9258	217	15	54	54	NUM
ap-9258	217	16	cos	cos	PROPN
ap-9258	217	17	(	(	PUNCT
ap-9258	217	18	kx	kx	PROPN
ap-9258	217	19	sin	sin	PROPN
ap-9258	217	20	θ	θ	PROPN
ap-9258	217	21	)	)	PUNCT
ap-9258	217	22	·	·	PUNCT
ap-9258	217	23	{	{	PUNCT
ap-9258	217	24	(	(	PUNCT
ap-9258	217	25	1	1	NUM
ap-9258	217	26	+	+	NUM
ap-9258	217	27	tan	tan	PROPN
ap-9258	217	28	54	54	NUM
ap-9258	217	29	tan	tan	NOUN
ap-9258	217	30	18	18	NUM
ap-9258	217	31	)	)	PUNCT
ap-9258	217	32	ap	ap	NOUN
ap-9258	218	1	−	−	PROPN
ap-9258	218	2	x	x	SYM
ap-9258	218	3	tan	tan	PROPN
ap-9258	218	4	18	18	NUM
ap-9258	218	5	}	}	PUNCT
ap-9258	218	6	dx	dx	PROPN
ap-9258	218	7	(	(	PUNCT
ap-9258	218	8	33	33	NUM
ap-9258	218	9	)	)	PUNCT
ap-9258	218	10	=	=	NOUN
ap-9258	219	1	i	i	PRON
ap-9258	219	2	a	a	DET
ap-9258	219	3	r	r	NOUN
ap-9258	219	4	2ei(ωt−kr	2ei(ωt−kr	NOUN
ap-9258	219	5	)	)	PUNCT
ap-9258	219	6	{	{	PUNCT
ap-9258	219	7	(	(	PUNCT
ap-9258	219	8	1	1	NUM
ap-9258	219	9	+	+	NUM
ap-9258	219	10	tan	tan	PROPN
ap-9258	219	11	54	54	NUM
ap-9258	219	12	tan	tan	NOUN
ap-9258	219	13	18	18	NUM
ap-9258	219	14	)	)	PUNCT
ap-9258	219	15	ap	ap	NOUN
ap-9258	219	16	(	(	PUNCT
ap-9258	219	17	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	219	18	sin	sin	NOUN
ap-9258	219	19	(	(	PUNCT
ap-9258	219	20	kx	kx	PROPN
ap-9258	219	21	sin	sin	PROPN
ap-9258	219	22	θ	θ	PROPN
ap-9258	219	23	)	)	PUNCT
ap-9258	220	1	k	k	NOUN
ap-9258	220	2	sin	sin	NOUN
ap-9258	220	3	θ	θ	PROPN
ap-9258	220	4	∣∣∣∣	∣∣∣∣	PROPN
ap-9258	220	5	ap	ap	PROPN
ap-9258	220	6	sec	sec	PROPN
ap-9258	220	7	54	54	NUM
ap-9258	220	8	−ap	−ap	PROPN
ap-9258	220	9	tan	tan	PROPN
ap-9258	220	10	54	54	NUM
ap-9258	220	11	)	)	PUNCT
ap-9258	221	1	−	−	PROPN
ap-9258	221	2	tan	tan	PROPN
ap-9258	221	3	18	18	NUM
ap-9258	221	4	(	(	PUNCT
ap-9258	221	5	∣∣∣∣x	∣∣∣∣x	NOUN
ap-9258	221	6	sin	sin	NOUN
ap-9258	221	7	(	(	PUNCT
ap-9258	221	8	kx	kx	PROPN
ap-9258	221	9	sin	sin	PROPN
ap-9258	221	10	θ	θ	PROPN
ap-9258	221	11	)	)	PUNCT
ap-9258	221	12	k	k	NOUN
ap-9258	221	13	sin	sin	NOUN
ap-9258	221	14	θ	θ	PROPN
ap-9258	221	15	∣∣∣∣	∣∣∣∣	PROPN
ap-9258	221	16	ap	ap	PROPN
ap-9258	221	17	sec	sec	PROPN
ap-9258	221	18	54	54	NUM
ap-9258	221	19	−ap	−ap	PROPN
ap-9258	221	20	tan	tan	PROPN
ap-9258	221	21	54	54	NUM
ap-9258	221	22	)	)	PUNCT
ap-9258	222	1	−	−	PROPN
ap-9258	222	2	tan	tan	PROPN
ap-9258	222	3	18	18	NUM
ap-9258	222	4	(	(	PUNCT
ap-9258	222	5	∣∣∣∣cos	∣∣∣∣cos	PROPN
ap-9258	222	6	(	(	PUNCT
ap-9258	222	7	kx	kx	PROPN
ap-9258	222	8	sin	sin	PROPN
ap-9258	222	9	θ	θ	PROPN
ap-9258	222	10	)	)	PUNCT
ap-9258	222	11	k2	k2	ADJ
ap-9258	222	12	sin2	sin2	NOUN
ap-9258	222	13	θ	θ	PROPN
ap-9258	222	14	∣∣∣∣	∣∣∣∣	PROPN
ap-9258	222	15	ap	ap	PROPN
ap-9258	222	16	sec	sec	PROPN
ap-9258	222	17	54	54	NUM
ap-9258	222	18	−ap	−ap	PROPN
ap-9258	222	19	tan	tan	PROPN
ap-9258	222	20	54	54	NUM
ap-9258	222	21	)	)	PUNCT
ap-9258	222	22	}	}	PUNCT
ap-9258	222	23	(	(	PUNCT
ap-9258	222	24	34	34	NUM
ap-9258	222	25	)	)	PUNCT
ap-9258	222	26	=	=	NOUN
ap-9258	223	1	i	i	PRON
ap-9258	223	2	a	a	DET
ap-9258	223	3	r	r	NOUN
ap-9258	223	4	2ei(ωt−kr	2ei(ωt−kr	NUM
ap-9258	223	5	)	)	PUNCT
ap-9258	223	6	[	[	PUNCT
ap-9258	223	7	(	(	PUNCT
ap-9258	223	8	1	1	NUM
ap-9258	223	9	+	+	NUM
ap-9258	223	10	tan	tan	PROPN
ap-9258	223	11	54	54	NUM
ap-9258	223	12	tan	tan	NOUN
ap-9258	223	13	18	18	NUM
ap-9258	223	14	)	)	PUNCT
ap-9258	223	15	ap	ap	PROPN
ap-9258	223	16	{	{	PUNCT
ap-9258	223	17	sin	sin	NOUN
ap-9258	223	18	(	(	PUNCT
ap-9258	223	19	kap	kap	NOUN
ap-9258	223	20	sec	sec	PROPN
ap-9258	223	21	54	54	NUM
ap-9258	223	22	sin	sin	NOUN
ap-9258	223	23	θ	θ	NOUN
ap-9258	223	24	)	)	PUNCT
ap-9258	223	25	+	+	CCONJ
ap-9258	223	26	sin	sin	NOUN
ap-9258	223	27	(	(	PUNCT
ap-9258	223	28	kap	kap	NOUN
ap-9258	223	29	tan	tan	PROPN
ap-9258	223	30	54	54	NUM
ap-9258	223	31	sin	sin	NOUN
ap-9258	223	32	θ	θ	NOUN
ap-9258	223	33	)	)	PUNCT
ap-9258	224	1	k	k	NOUN
ap-9258	224	2	sin	sin	NOUN
ap-9258	224	3	θ	θ	NOUN
ap-9258	224	4	}	}	PUNCT
ap-9258	224	5	−	−	PROPN
ap-9258	224	6	{	{	PUNCT
ap-9258	224	7	(	(	PUNCT
ap-9258	224	8	tan	tan	PROPN
ap-9258	224	9	18	18	NUM
ap-9258	224	10	sec	sec	PROPN
ap-9258	224	11	54	54	NUM
ap-9258	224	12	)	)	PUNCT
ap-9258	224	13	ap	ap	PROPN
ap-9258	224	14	sin	sin	NOUN
ap-9258	224	15	(	(	PUNCT
ap-9258	224	16	kap	kap	PROPN
ap-9258	224	17	sec	sec	PROPN
ap-9258	224	18	54	54	NUM
ap-9258	224	19	sin	sin	NOUN
ap-9258	224	20	θ	θ	NOUN
ap-9258	224	21	)	)	PUNCT
ap-9258	224	22	−	−	PROPN
ap-9258	225	1	(	(	PUNCT
ap-9258	225	2	tan	tan	PROPN
ap-9258	225	3	18	18	NUM
ap-9258	225	4	tan	tan	PROPN
ap-9258	225	5	54	54	NUM
ap-9258	225	6	)	)	PUNCT
ap-9258	225	7	ap	ap	PROPN
ap-9258	225	8	sin	sin	NOUN
ap-9258	225	9	(	(	PUNCT
ap-9258	225	10	kap	kap	NOUN
ap-9258	225	11	tan	tan	PROPN
ap-9258	225	12	54	54	NUM
ap-9258	225	13	sin	sin	NOUN
ap-9258	225	14	θ	θ	NOUN
ap-9258	225	15	)	)	PUNCT
ap-9258	225	16	k	k	NOUN
ap-9258	225	17	sin	sin	NOUN
ap-9258	225	18	θ	θ	NOUN
ap-9258	225	19	}	}	PUNCT
ap-9258	225	20	−	−	PROPN
ap-9258	225	21	tan	tan	NOUN
ap-9258	225	22	18	18	NUM
ap-9258	225	23	{	{	PUNCT
ap-9258	225	24	cos	cos	PROPN
ap-9258	225	25	(	(	PUNCT
ap-9258	225	26	kap	kap	PROPN
ap-9258	225	27	sec	sec	PROPN
ap-9258	225	28	54	54	NUM
ap-9258	225	29	sin	sin	NOUN
ap-9258	225	30	θ	θ	NOUN
ap-9258	225	31	)	)	PUNCT
ap-9258	225	32	−	−	PROPN
ap-9258	226	1	cos	cos	PROPN
ap-9258	226	2	(	(	PUNCT
ap-9258	226	3	kap	kap	PROPN
ap-9258	226	4	tan	tan	PROPN
ap-9258	226	5	54	54	NUM
ap-9258	226	6	sin	sin	NOUN
ap-9258	226	7	θ	θ	NOUN
ap-9258	226	8	)	)	PUNCT
ap-9258	226	9	k2	k2	ADJ
ap-9258	226	10	sin2	sin2	NOUN
ap-9258	226	11	θ	θ	PROPN
ap-9258	226	12	}	}	PUNCT
ap-9258	226	13	]	]	PUNCT
ap-9258	226	14	(	(	PUNCT
ap-9258	226	15	35	35	NUM
ap-9258	226	16	)	)	PUNCT
ap-9258	226	17	476	476	NUM
ap-9258	226	18	vol	vol	NOUN
ap-9258	226	19	.	.	PUNCT
ap-9258	227	1	64	64	NUM
ap-9258	227	2	no	no	NOUN
ap-9258	227	3	.	.	PUNCT
ap-9258	228	1	5/2024	5/2024	ADJ
ap-9258	228	2	acoustic	acoustic	ADJ
ap-9258	228	3	radiation	radiation	NOUN
ap-9258	228	4	beam	beam	NOUN
ap-9258	228	5	patterns	pattern	NOUN
ap-9258	228	6	of	of	ADP
ap-9258	228	7	different	different	ADJ
ap-9258	228	8	polygonal	polygonal	NOUN
ap-9258	228	9	.	.	PUNCT
ap-9258	228	10	.	.	PUNCT
ap-9258	228	11	.	.	PUNCT
ap-9258	229	1	=	=	PRON
ap-9258	230	1	i	i	PRON
ap-9258	230	2	a	a	DET
ap-9258	230	3	r	r	NOUN
ap-9258	230	4	2ei(ωt−kr	2ei(ωt−kr	NUM
ap-9258	230	5	)	)	PUNCT
ap-9258	230	6	[	[	PUNCT
ap-9258	230	7	(	(	PUNCT
ap-9258	230	8	1	1	NUM
ap-9258	230	9	+	+	NUM
ap-9258	230	10	tan	tan	PROPN
ap-9258	230	11	54	54	NUM
ap-9258	230	12	tan	tan	NOUN
ap-9258	230	13	18	18	NUM
ap-9258	230	14	−	−	PROPN
ap-9258	230	15	tan	tan	PROPN
ap-9258	230	16	18	18	NUM
ap-9258	230	17	sec	sec	PROPN
ap-9258	230	18	54	54	NUM
ap-9258	230	19	)	)	PUNCT
ap-9258	230	20	ap	ap	PROPN
ap-9258	230	21	{	{	PUNCT
ap-9258	230	22	sin	sin	NOUN
ap-9258	230	23	(	(	PUNCT
ap-9258	230	24	kap	kap	NOUN
ap-9258	230	25	sec	sec	PROPN
ap-9258	230	26	54	54	NUM
ap-9258	230	27	sin	sin	NOUN
ap-9258	230	28	θ	θ	NOUN
ap-9258	230	29	)	)	PUNCT
ap-9258	230	30	k	k	NOUN
ap-9258	230	31	sin	sin	NOUN
ap-9258	230	32	θ	θ	NOUN
ap-9258	230	33	}	}	PUNCT
ap-9258	231	1	+	+	CCONJ
ap-9258	231	2	(	(	PUNCT
ap-9258	231	3	1	1	NUM
ap-9258	231	4	+	+	SYM
ap-9258	231	5	2	2	NUM
ap-9258	231	6	tan	tan	PROPN
ap-9258	231	7	54	54	NUM
ap-9258	231	8	tan	tan	NOUN
ap-9258	231	9	18	18	NUM
ap-9258	231	10	)	)	PUNCT
ap-9258	231	11	ap	ap	PROPN
ap-9258	231	12	{	{	PUNCT
ap-9258	231	13	sin	sin	NOUN
ap-9258	231	14	(	(	PUNCT
ap-9258	231	15	kap	kap	NOUN
ap-9258	231	16	tan	tan	PROPN
ap-9258	231	17	54	54	NUM
ap-9258	231	18	sin	sin	NOUN
ap-9258	231	19	θ	θ	NOUN
ap-9258	231	20	)	)	PUNCT
ap-9258	231	21	k	k	NOUN
ap-9258	231	22	sin	sin	NOUN
ap-9258	231	23	θ	θ	NOUN
ap-9258	231	24	}	}	PUNCT
ap-9258	231	25	+	+	CCONJ
ap-9258	231	26	2	2	NUM
ap-9258	231	27	tan	tan	NOUN
ap-9258	231	28	18	18	NUM
ap-9258	231	29	k2	k2	ADJ
ap-9258	231	30	sin2	sin2	NOUN
ap-9258	231	31	θ	θ	PROPN
ap-9258	231	32	[	[	PUNCT
ap-9258	231	33	sin	sin	NOUN
ap-9258	231	34	{	{	PUNCT
ap-9258	231	35	k	k	PROPN
ap-9258	231	36	(	(	PUNCT
ap-9258	231	37	sec	sec	PROPN
ap-9258	231	38	54	54	NUM
ap-9258	231	39	+	+	CCONJ
ap-9258	231	40	tan	tan	PROPN
ap-9258	231	41	54	54	NUM
ap-9258	231	42	2	2	NUM
ap-9258	231	43	)	)	PUNCT
ap-9258	231	44	ap	ap	PROPN
ap-9258	231	45	sin	sin	NOUN
ap-9258	231	46	θ	θ	PROPN
ap-9258	231	47	}	}	PUNCT
ap-9258	231	48	sin	sin	NOUN
ap-9258	231	49	{	{	PUNCT
ap-9258	231	50	k	k	X
ap-9258	231	51	(	(	PUNCT
ap-9258	231	52	sec	sec	PROPN
ap-9258	231	53	54	54	NUM
ap-9258	231	54	−	−	NOUN
ap-9258	231	55	tan	tan	PROPN
ap-9258	231	56	54	54	NUM
ap-9258	231	57	2	2	NUM
ap-9258	231	58	)	)	PUNCT
ap-9258	231	59	a	a	DET
ap-9258	231	60	p	p	NOUN
ap-9258	231	61	sin	sin	NOUN
ap-9258	231	62	θ	θ	NOUN
ap-9258	231	63	}	}	PUNCT
ap-9258	231	64	]	]	PUNCT
ap-9258	231	65	]	]	PUNCT
ap-9258	231	66	,	,	PUNCT
ap-9258	231	67	(	(	PUNCT
ap-9258	231	68	36	36	NUM
ap-9258	231	69	)	)	PUNCT
ap-9258	231	70	pp	pp	ADP
ap-9258	232	1	=	=	PUNCT
ap-9258	232	2	i	i	PRON
ap-9258	232	3	a	a	DET
ap-9258	232	4	r	r	NOUN
ap-9258	232	5	2ap	2ap	NOUN
ap-9258	232	6	2ei(ωt−kr	2ei(ωt−kr	NOUN
ap-9258	232	7	)	)	PUNCT
ap-9258	232	8	sec	sec	ADP
ap-9258	232	9	54	54	NUM
ap-9258	232	10	{	{	PUNCT
ap-9258	232	11	1	1	NUM
ap-9258	232	12	+	+	NUM
ap-9258	232	13	tan	tan	PROPN
ap-9258	232	14	18	18	NUM
ap-9258	232	15	(	(	PUNCT
ap-9258	232	16	tan	tan	PROPN
ap-9258	232	17	54	54	NUM
ap-9258	232	18	−	−	NOUN
ap-9258	232	19	sec	sec	PROPN
ap-9258	232	20	54	54	NUM
ap-9258	232	21	)	)	PUNCT
ap-9258	232	22	}	}	PUNCT
ap-9258	232	23	{	{	PUNCT
ap-9258	232	24	sin	sin	NOUN
ap-9258	232	25	(	(	PUNCT
ap-9258	232	26	kap	kap	NOUN
ap-9258	232	27	sec	sec	PROPN
ap-9258	232	28	54	54	NUM
ap-9258	232	29	sin	sin	NOUN
ap-9258	232	30	θ	θ	NOUN
ap-9258	232	31	)	)	PUNCT
ap-9258	232	32	kap	kap	NOUN
ap-9258	232	33	sec	sec	PROPN
ap-9258	232	34	54	54	NUM
ap-9258	232	35	sin	sin	NOUN
ap-9258	232	36	θ	θ	NOUN
ap-9258	232	37	}	}	PUNCT
ap-9258	233	1	+	+	CCONJ
ap-9258	233	2	tan	tan	PROPN
ap-9258	233	3	54	54	NUM
ap-9258	233	4	(	(	PUNCT
ap-9258	233	5	1	1	NUM
ap-9258	233	6	+	+	SYM
ap-9258	233	7	2	2	NUM
ap-9258	233	8	tan	tan	PROPN
ap-9258	233	9	54	54	NUM
ap-9258	233	10	tan	tan	NOUN
ap-9258	233	11	18	18	NUM
ap-9258	233	12	)	)	PUNCT
ap-9258	233	13	{	{	PUNCT
ap-9258	233	14	sin	sin	NOUN
ap-9258	233	15	(	(	PUNCT
ap-9258	233	16	kap	kap	NOUN
ap-9258	233	17	tan	tan	PROPN
ap-9258	233	18	54	54	NUM
ap-9258	233	19	sin	sin	NOUN
ap-9258	233	20	θ	θ	NOUN
ap-9258	233	21	)	)	PUNCT
ap-9258	233	22	kap	kap	PROPN
ap-9258	233	23	tan	tan	PROPN
ap-9258	233	24	54	54	NUM
ap-9258	233	25	sin	sin	NOUN
ap-9258	233	26	θ	θ	NOUN
ap-9258	233	27	}	}	PUNCT
ap-9258	234	1	+	+	NOUN
ap-9258	234	2	tan	tan	PROPN
ap-9258	234	3	18	18	NUM
ap-9258	234	4	2	2	NUM
ap-9258	234	5			NOUN
ap-9258	234	6	sin	sin	NOUN
ap-9258	234	7	{	{	PUNCT
ap-9258	234	8	k	k	X
ap-9258	234	9	(	(	PUNCT
ap-9258	234	10	sec	sec	PROPN
ap-9258	234	11	54+tan	54+tan	PROPN
ap-9258	234	12	54	54	NUM
ap-9258	234	13	2	2	NUM
ap-9258	234	14	)	)	PUNCT
ap-9258	234	15	a	a	DET
ap-9258	234	16	p	p	NOUN
ap-9258	234	17	sin	sin	NOUN
ap-9258	234	18	θ	θ	NOUN
ap-9258	234	19	}	}	PUNCT
ap-9258	234	20	k	k	PROPN
ap-9258	234	21	(	(	PUNCT
ap-9258	234	22	sec	sec	PROPN
ap-9258	234	23	54+tan	54+tan	PROPN
ap-9258	234	24	54	54	NUM
ap-9258	234	25	2	2	NUM
ap-9258	234	26	)	)	PUNCT
ap-9258	234	27	a	a	DET
ap-9258	234	28	p	p	NOUN
ap-9258	234	29	sin	sin	NOUN
ap-9258	234	30	θ	θ	PROPN
ap-9258	234	31	·	·	PUNCT
ap-9258	234	32	sin	sin	NOUN
ap-9258	234	33	{	{	PUNCT
ap-9258	234	34	k	k	X
ap-9258	234	35	(	(	PUNCT
ap-9258	234	36	sec	sec	PROPN
ap-9258	234	37	54−tan	54−tan	PROPN
ap-9258	234	38	54	54	NUM
ap-9258	234	39	2	2	NUM
ap-9258	234	40	)	)	PUNCT
ap-9258	234	41	a	a	DET
ap-9258	234	42	p	p	NOUN
ap-9258	234	43	sin	sin	NOUN
ap-9258	234	44	θ	θ	NOUN
ap-9258	234	45	}	}	PUNCT
ap-9258	234	46	k	k	PROPN
ap-9258	235	1	(	(	PUNCT
ap-9258	235	2	sec	sec	PROPN
ap-9258	235	3	54−tan	54−tan	PROPN
ap-9258	235	4	54	54	NUM
ap-9258	235	5	2	2	NUM
ap-9258	235	6	)	)	PUNCT
ap-9258	235	7	a	a	DET
ap-9258	235	8	p	p	NOUN
ap-9258	235	9	sin	sin	NOUN
ap-9258	235	10	θ	θ	PROPN
ap-9258	235	11			PROPN
ap-9258	235	12	,	,	PUNCT
ap-9258	235	13	(	(	PUNCT
ap-9258	235	14	37	37	NUM
ap-9258	235	15	)	)	PUNCT
ap-9258	235	16	hp	hp	NOUN
ap-9258	235	17	=	=	PUNCT
ap-9258	235	18	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ap-9258	235	19	sec	sec	PROPN
ap-9258	235	20	54	54	NUM
ap-9258	235	21	{	{	PUNCT
ap-9258	235	22	1	1	NUM
ap-9258	235	23	+	+	NUM
ap-9258	235	24	tan	tan	PROPN
ap-9258	235	25	18	18	NUM
ap-9258	235	26	(	(	PUNCT
ap-9258	235	27	tan	tan	PROPN
ap-9258	235	28	54	54	NUM
ap-9258	235	29	−	−	NOUN
ap-9258	235	30	sec	sec	PROPN
ap-9258	235	31	54	54	NUM
ap-9258	235	32	)	)	PUNCT
ap-9258	235	33	}	}	PUNCT
ap-9258	235	34	{	{	PUNCT
ap-9258	235	35	sin	sin	NOUN
ap-9258	235	36	(	(	PUNCT
ap-9258	235	37	kap	kap	NOUN
ap-9258	235	38	sec	sec	PROPN
ap-9258	235	39	54	54	NUM
ap-9258	235	40	sin	sin	NOUN
ap-9258	235	41	θ	θ	NOUN
ap-9258	235	42	)	)	PUNCT
ap-9258	235	43	kap	kap	NOUN
ap-9258	235	44	sec	sec	PROPN
ap-9258	235	45	54	54	NUM
ap-9258	235	46	sin	sin	NOUN
ap-9258	235	47	θ	θ	NOUN
ap-9258	235	48	}	}	PUNCT
ap-9258	236	1	+	+	CCONJ
ap-9258	236	2	tan	tan	PROPN
ap-9258	236	3	54	54	NUM
ap-9258	236	4	(	(	PUNCT
ap-9258	236	5	1	1	NUM
ap-9258	236	6	+	+	SYM
ap-9258	236	7	2	2	NUM
ap-9258	236	8	tan	tan	PROPN
ap-9258	236	9	54	54	NUM
ap-9258	236	10	tan	tan	NOUN
ap-9258	236	11	18	18	NUM
ap-9258	236	12	)	)	PUNCT
ap-9258	236	13	{	{	PUNCT
ap-9258	236	14	sin	sin	NOUN
ap-9258	236	15	(	(	PUNCT
ap-9258	236	16	kap	kap	NOUN
ap-9258	236	17	tan	tan	PROPN
ap-9258	236	18	54	54	NUM
ap-9258	236	19	sin	sin	NOUN
ap-9258	236	20	θ	θ	NOUN
ap-9258	236	21	)	)	PUNCT
ap-9258	236	22	kap	kap	PROPN
ap-9258	236	23	tan	tan	PROPN
ap-9258	236	24	54	54	NUM
ap-9258	236	25	sin	sin	NOUN
ap-9258	236	26	θ	θ	NOUN
ap-9258	236	27	}	}	PUNCT
ap-9258	237	1	+	+	NOUN
ap-9258	237	2	tan	tan	PROPN
ap-9258	237	3	18	18	NUM
ap-9258	237	4	2	2	NUM
ap-9258	237	5			NOUN
ap-9258	237	6	sin	sin	NOUN
ap-9258	237	7	{	{	PUNCT
ap-9258	237	8	k	k	X
ap-9258	237	9	(	(	PUNCT
ap-9258	237	10	sec	sec	PROPN
ap-9258	237	11	54+tan	54+tan	PROPN
ap-9258	237	12	54	54	NUM
ap-9258	237	13	2	2	NUM
ap-9258	237	14	)	)	PUNCT
ap-9258	237	15	a	a	DET
ap-9258	237	16	p	p	NOUN
ap-9258	237	17	sin	sin	NOUN
ap-9258	237	18	θ	θ	NOUN
ap-9258	237	19	}	}	PUNCT
ap-9258	237	20	k	k	PROPN
ap-9258	237	21	(	(	PUNCT
ap-9258	237	22	sec	sec	PROPN
ap-9258	237	23	54+tan	54+tan	PROPN
ap-9258	237	24	54	54	NUM
ap-9258	237	25	2	2	NUM
ap-9258	237	26	)	)	PUNCT
ap-9258	237	27	a	a	DET
ap-9258	237	28	p	p	NOUN
ap-9258	237	29	sin	sin	NOUN
ap-9258	237	30	θ	θ	PROPN
ap-9258	237	31	·	·	PUNCT
ap-9258	237	32	sin	sin	NOUN
ap-9258	237	33	{	{	PUNCT
ap-9258	237	34	k	k	X
ap-9258	237	35	(	(	PUNCT
ap-9258	237	36	sec	sec	PROPN
ap-9258	237	37	54−tan	54−tan	PROPN
ap-9258	237	38	54	54	NUM
ap-9258	237	39	2	2	NUM
ap-9258	237	40	)	)	PUNCT
ap-9258	237	41	a	a	DET
ap-9258	237	42	p	p	NOUN
ap-9258	237	43	sin	sin	NOUN
ap-9258	237	44	θ	θ	NOUN
ap-9258	237	45	}	}	PUNCT
ap-9258	237	46	k	k	PROPN
ap-9258	238	1	(	(	PUNCT
ap-9258	238	2	sec	sec	PROPN
ap-9258	238	3	54−tan	54−tan	PROPN
ap-9258	238	4	54	54	NUM
ap-9258	238	5	2	2	NUM
ap-9258	238	6	)	)	PUNCT
ap-9258	238	7	a	a	DET
ap-9258	238	8	p	p	NOUN
ap-9258	238	9	sin	sin	NOUN
ap-9258	238	10	θ	θ	PROPN
ap-9258	238	11	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ap-9258	238	12	(	(	PUNCT
ap-9258	238	13	38	38	NUM
ap-9258	238	14	)	)	PUNCT
ap-9258	238	15	=	=	SYM
ap-9258	239	1	∣∣∣∣∣∣sec	∣∣∣∣∣∣sec	PROPN
ap-9258	239	2	54	54	NUM
ap-9258	239	3	{	{	PUNCT
ap-9258	239	4	1	1	NUM
ap-9258	239	5	+	+	CCONJ
ap-9258	239	6	(	(	PUNCT
ap-9258	239	7	sec	sec	PROPN
ap-9258	239	8	54	54	NUM
ap-9258	239	9	−	−	PROPN
ap-9258	239	10	tan	tan	PROPN
ap-9258	239	11	54	54	NUM
ap-9258	239	12	tan	tan	PROPN
ap-9258	239	13	108	108	NUM
ap-9258	239	14	)	)	PUNCT
ap-9258	239	15	}	}	PUNCT
ap-9258	239	16	{	{	PUNCT
ap-9258	239	17	sin	sin	NOUN
ap-9258	239	18	(	(	PUNCT
ap-9258	239	19	kap	kap	NOUN
ap-9258	239	20	sec	sec	PROPN
ap-9258	239	21	54	54	NUM
ap-9258	239	22	sin	sin	NOUN
ap-9258	239	23	θ	θ	NOUN
ap-9258	239	24	)	)	PUNCT
ap-9258	239	25	kap	kap	NOUN
ap-9258	239	26	sec	sec	PROPN
ap-9258	239	27	54	54	NUM
ap-9258	239	28	sin	sin	NOUN
ap-9258	239	29	θ	θ	NOUN
ap-9258	239	30	}	}	PUNCT
ap-9258	239	31	+	+	CCONJ
ap-9258	239	32	tan	tan	PROPN
ap-9258	239	33	54	54	NUM
ap-9258	239	34	(	(	PUNCT
ap-9258	239	35	1	1	NUM
ap-9258	239	36	−	−	NUM
ap-9258	239	37	2	2	NUM
ap-9258	239	38	tan	tan	PROPN
ap-9258	239	39	54	54	NUM
ap-9258	239	40	tan	tan	PROPN
ap-9258	239	41	108	108	NUM
ap-9258	239	42	)	)	PUNCT
ap-9258	239	43	{	{	PUNCT
ap-9258	239	44	sin	sin	NOUN
ap-9258	239	45	(	(	PUNCT
ap-9258	239	46	kap	kap	NOUN
ap-9258	239	47	tan	tan	PROPN
ap-9258	239	48	54	54	NUM
ap-9258	239	49	sin	sin	NOUN
ap-9258	239	50	θ	θ	NOUN
ap-9258	239	51	)	)	PUNCT
ap-9258	239	52	kap	kap	PROPN
ap-9258	239	53	tan	tan	PROPN
ap-9258	239	54	54	54	NUM
ap-9258	239	55	sin	sin	NOUN
ap-9258	239	56	θ	θ	NOUN
ap-9258	239	57	}	}	PUNCT
ap-9258	239	58	−	−	PROPN
ap-9258	239	59	1	1	NUM
ap-9258	239	60	2	2	NUM
ap-9258	239	61	tan	tan	NOUN
ap-9258	239	62	108	108	NUM
ap-9258	239	63			NOUN
ap-9258	239	64	sin	sin	NOUN
ap-9258	239	65	{	{	PUNCT
ap-9258	239	66	k	k	X
ap-9258	239	67	(	(	PUNCT
ap-9258	239	68	sec	sec	PROPN
ap-9258	239	69	54+tan	54+tan	PROPN
ap-9258	239	70	54	54	NUM
ap-9258	239	71	2	2	NUM
ap-9258	239	72	)	)	PUNCT
ap-9258	239	73	a	a	DET
ap-9258	239	74	p	p	NOUN
ap-9258	239	75	sin	sin	NOUN
ap-9258	239	76	θ	θ	NOUN
ap-9258	239	77	}	}	PUNCT
ap-9258	239	78	k	k	PROPN
ap-9258	240	1	(	(	PUNCT
ap-9258	240	2	sec	sec	PROPN
ap-9258	240	3	54+tan	54+tan	PROPN
ap-9258	240	4	54	54	NUM
ap-9258	240	5	2	2	NUM
ap-9258	240	6	)	)	PUNCT
ap-9258	240	7	a	a	DET
ap-9258	240	8	p	p	NOUN
ap-9258	240	9	sin	sin	NOUN
ap-9258	240	10	θ	θ	PROPN
ap-9258	240	11	·	·	PUNCT
ap-9258	240	12	sin	sin	NOUN
ap-9258	240	13	{	{	PUNCT
ap-9258	240	14	k	k	X
ap-9258	240	15	(	(	PUNCT
ap-9258	240	16	sec	sec	PROPN
ap-9258	240	17	54−tan	54−tan	PROPN
ap-9258	240	18	54	54	NUM
ap-9258	240	19	2	2	NUM
ap-9258	240	20	)	)	PUNCT
ap-9258	240	21	a	a	DET
ap-9258	240	22	p	p	NOUN
ap-9258	240	23	sin	sin	NOUN
ap-9258	240	24	θ	θ	NOUN
ap-9258	240	25	}	}	PUNCT
ap-9258	240	26	k	k	PROPN
ap-9258	240	27	(	(	PUNCT
ap-9258	240	28	sec	sec	PROPN
ap-9258	240	29	54−tan	54−tan	PROPN
ap-9258	240	30	54	54	NUM
ap-9258	240	31	2	2	NUM
ap-9258	240	32	)	)	PUNCT
ap-9258	240	33	a	a	DET
ap-9258	240	34	p	p	NOUN
ap-9258	240	35	sin	sin	NOUN
ap-9258	240	36	θ	θ	PROPN
ap-9258	240	37	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ap-9258	240	38	,	,	PUNCT
ap-9258	240	39	(	(	PUNCT
ap-9258	240	40	39	39	NUM
ap-9258	240	41	)	)	PUNCT
ap-9258	240	42	hp	hp	NOUN
ap-9258	240	43	=	=	SYM
ap-9258	240	44	∣∣∣∣∣∣sec	∣∣∣∣∣∣sec	PROPN
ap-9258	240	45	54	54	NUM
ap-9258	240	46	{	{	PUNCT
ap-9258	240	47	1	1	NUM
ap-9258	240	48	+	+	CCONJ
ap-9258	240	49	(	(	PUNCT
ap-9258	240	50	sec	sec	PROPN
ap-9258	240	51	54	54	NUM
ap-9258	240	52	−	−	PROPN
ap-9258	240	53	tan	tan	PROPN
ap-9258	240	54	54	54	NUM
ap-9258	240	55	tan	tan	PROPN
ap-9258	240	56	108	108	NUM
ap-9258	240	57	)	)	PUNCT
ap-9258	240	58	}	}	PUNCT
ap-9258	240	59	{	{	PUNCT
ap-9258	240	60	sin	sin	NOUN
ap-9258	240	61	(	(	PUNCT
ap-9258	240	62	kap	kap	NOUN
ap-9258	240	63	sec	sec	PROPN
ap-9258	240	64	54	54	NUM
ap-9258	240	65	sin	sin	NOUN
ap-9258	240	66	θ	θ	NOUN
ap-9258	240	67	)	)	PUNCT
ap-9258	240	68	kap	kap	NOUN
ap-9258	240	69	sec	sec	PROPN
ap-9258	240	70	54	54	NUM
ap-9258	240	71	sin	sin	NOUN
ap-9258	240	72	θ	θ	NOUN
ap-9258	240	73	}	}	PUNCT
ap-9258	240	74	+	+	CCONJ
ap-9258	240	75	tan3	tan3	NOUN
ap-9258	240	76	54	54	NUM
ap-9258	240	77	{	{	PUNCT
ap-9258	240	78	sin	sin	NOUN
ap-9258	240	79	(	(	PUNCT
ap-9258	240	80	kap	kap	NOUN
ap-9258	240	81	tan	tan	PROPN
ap-9258	240	82	54	54	NUM
ap-9258	240	83	sin	sin	NOUN
ap-9258	240	84	θ	θ	NOUN
ap-9258	240	85	)	)	PUNCT
ap-9258	240	86	kap	kap	PROPN
ap-9258	240	87	tan	tan	PROPN
ap-9258	240	88	54	54	NUM
ap-9258	240	89	sin	sin	NOUN
ap-9258	240	90	θ	θ	NOUN
ap-9258	240	91	}	}	PUNCT
ap-9258	240	92	−	−	PROPN
ap-9258	240	93	1	1	NUM
ap-9258	240	94	2	2	NUM
ap-9258	240	95	tan	tan	NOUN
ap-9258	240	96	108	108	NUM
ap-9258	240	97			NOUN
ap-9258	240	98	sin	sin	NOUN
ap-9258	240	99	{	{	PUNCT
ap-9258	240	100	k	k	X
ap-9258	240	101	(	(	PUNCT
ap-9258	240	102	sec	sec	PROPN
ap-9258	240	103	54+tan	54+tan	PROPN
ap-9258	240	104	54	54	NUM
ap-9258	240	105	2	2	NUM
ap-9258	240	106	)	)	PUNCT
ap-9258	240	107	a	a	DET
ap-9258	240	108	p	p	NOUN
ap-9258	240	109	sin	sin	NOUN
ap-9258	240	110	θ	θ	NOUN
ap-9258	240	111	}	}	PUNCT
ap-9258	240	112	k	k	PROPN
ap-9258	241	1	(	(	PUNCT
ap-9258	241	2	sec	sec	PROPN
ap-9258	241	3	54+tan	54+tan	PROPN
ap-9258	241	4	54	54	NUM
ap-9258	241	5	2	2	NUM
ap-9258	241	6	)	)	PUNCT
ap-9258	241	7	a	a	DET
ap-9258	241	8	p	p	NOUN
ap-9258	241	9	sin	sin	NOUN
ap-9258	241	10	θ	θ	PROPN
ap-9258	241	11	·	·	PUNCT
ap-9258	241	12	sin	sin	NOUN
ap-9258	241	13	{	{	PUNCT
ap-9258	241	14	k	k	X
ap-9258	241	15	(	(	PUNCT
ap-9258	241	16	sec	sec	PROPN
ap-9258	241	17	54−tan	54−tan	PROPN
ap-9258	241	18	54	54	NUM
ap-9258	241	19	2	2	NUM
ap-9258	241	20	)	)	PUNCT
ap-9258	241	21	a	a	DET
ap-9258	241	22	p	p	NOUN
ap-9258	241	23	sin	sin	NOUN
ap-9258	241	24	θ	θ	NOUN
ap-9258	241	25	}	}	PUNCT
ap-9258	241	26	k	k	PROPN
ap-9258	241	27	(	(	PUNCT
ap-9258	241	28	sec	sec	PROPN
ap-9258	241	29	54−tan	54−tan	PROPN
ap-9258	241	30	54	54	NUM
ap-9258	241	31	2	2	NUM
ap-9258	241	32	)	)	PUNCT
ap-9258	241	33	a	a	DET
ap-9258	241	34	p	p	NOUN
ap-9258	241	35	sin	sin	NOUN
ap-9258	241	36	θ	θ	PROPN
ap-9258	241	37	∣∣∣∣∣∣.	∣∣∣∣∣∣.	PROPN
ap-9258	241	38	(	(	PUNCT
ap-9258	241	39	40	40	NUM
ap-9258	241	40	)	)	PUNCT
ap-9258	241	41	3.5	3.5	NUM
ap-9258	241	42	.	.	PUNCT
ap-9258	242	1	hexagonal	hexagonal	ADJ
ap-9258	242	2	piston	piston	NOUN
ap-9258	242	3	the	the	DET
ap-9258	242	4	position	position	NOUN
ap-9258	242	5	of	of	ADP
ap-9258	242	6	the	the	DET
ap-9258	242	7	centre	centre	NOUN
ap-9258	242	8	c	c	PROPN
ap-9258	242	9	of	of	ADP
ap-9258	242	10	a	a	DET
ap-9258	242	11	regular	regular	ADJ
ap-9258	242	12	hexagon	hexagon	NOUN
ap-9258	242	13	surface	surface	NOUN
ap-9258	242	14	geometry	geometry	NOUN
ap-9258	242	15	,	,	PUNCT
ap-9258	242	16	which	which	PRON
ap-9258	242	17	is	be	AUX
ap-9258	242	18	clearly	clearly	ADV
ap-9258	242	19	symmetrical	symmetrical	ADJ
ap-9258	242	20	,	,	PUNCT
ap-9258	242	21	is	be	AUX
ap-9258	242	22	shown	show	VERB
ap-9258	242	23	in	in	ADP
ap-9258	242	24	figure	figure	NOUN
ap-9258	242	25	8	8	NUM
ap-9258	242	26	.	.	PUNCT
ap-9258	243	1	the	the	DET
ap-9258	243	2	hsl	hsl	NOUN
ap-9258	243	3	,	,	PUNCT
ap-9258	243	4	ab	ab	PROPN
ap-9258	243	5	of	of	ADP
ap-9258	243	6	the	the	DET
ap-9258	243	7	acoustic	acoustic	ADJ
ap-9258	243	8	element	element	NOUN
ap-9258	243	9	on	on	ADP
ap-9258	243	10	the	the	DET
ap-9258	243	11	surface	surface	NOUN
ap-9258	243	12	can	can	AUX
ap-9258	243	13	be	be	AUX
ap-9258	243	14	found	find	VERB
ap-9258	243	15	using	use	VERB
ap-9258	243	16	the	the	DET
ap-9258	243	17	similar	similar	ADJ
ap-9258	243	18	triangles	triangle	NOUN
ap-9258	243	19	approach	approach	NOUN
ap-9258	243	20	as	as	SCONJ
ap-9258	243	21	shown	show	VERB
ap-9258	243	22	in	in	ADP
ap-9258	243	23	equation	equation	NOUN
ap-9258	243	24	(	(	PUNCT
ap-9258	243	25	41	41	NUM
ap-9258	243	26	)	)	PUNCT
ap-9258	243	27	.	.	PUNCT
ap-9258	244	1	the	the	DET
ap-9258	244	2	complex	complex	ADJ
ap-9258	244	3	component	component	NOUN
ap-9258	244	4	of	of	ADP
ap-9258	244	5	the	the	DET
ap-9258	244	6	pressure	pressure	NOUN
ap-9258	244	7	integral	integral	ADJ
ap-9258	244	8	px	px	NOUN
ap-9258	244	9	is	be	AUX
ap-9258	244	10	then	then	ADV
ap-9258	244	11	given	give	VERB
ap-9258	244	12	in	in	ADP
ap-9258	244	13	equation	equation	NOUN
ap-9258	244	14	(	(	PUNCT
ap-9258	244	15	42	42	NUM
ap-9258	244	16	)	)	PUNCT
ap-9258	244	17	and	and	CCONJ
ap-9258	244	18	evaluated	evaluate	VERB
ap-9258	244	19	in	in	ADP
ap-9258	244	20	equation	equation	NOUN
ap-9258	244	21	(	(	PUNCT
ap-9258	244	22	43	43	NUM
ap-9258	244	23	)	)	PUNCT
ap-9258	244	24	.	.	PUNCT
ap-9258	245	1	on	on	ADP
ap-9258	245	2	further	further	ADJ
ap-9258	245	3	simplification	simplification	NOUN
ap-9258	245	4	,	,	PUNCT
ap-9258	245	5	the	the	DET
ap-9258	245	6	middle	middle	NOUN
ap-9258	245	7	and	and	CCONJ
ap-9258	245	8	the	the	DET
ap-9258	245	9	last	last	ADJ
ap-9258	245	10	terms	term	NOUN
ap-9258	245	11	in	in	ADP
ap-9258	245	12	this	this	DET
ap-9258	245	13	equation	equation	NOUN
ap-9258	245	14	vanishes	vanish	VERB
ap-9258	245	15	and	and	CCONJ
ap-9258	245	16	the	the	DET
ap-9258	245	17	final	final	ADJ
ap-9258	245	18	expression	expression	NOUN
ap-9258	245	19	for	for	ADP
ap-9258	245	20	the	the	DET
ap-9258	245	21	acoustic	acoustic	ADJ
ap-9258	245	22	pressure	pressure	NOUN
ap-9258	245	23	then	then	ADV
ap-9258	245	24	becomes	become	VERB
ap-9258	245	25	equation	equation	NOUN
ap-9258	245	26	(	(	PUNCT
ap-9258	245	27	44	44	NUM
ap-9258	245	28	)	)	PUNCT
ap-9258	245	29	.	.	PUNCT
ap-9258	246	1	then	then	ADV
ap-9258	246	2	,	,	PUNCT
ap-9258	246	3	the	the	DET
ap-9258	246	4	directional	directional	ADJ
ap-9258	246	5	factor	factor	NOUN
ap-9258	246	6	is	be	AUX
ap-9258	246	7	isolated	isolate	VERB
ap-9258	246	8	as	as	ADP
ap-9258	246	9	equation	equation	NOUN
ap-9258	246	10	(	(	PUNCT
ap-9258	246	11	45	45	NUM
ap-9258	246	12	)	)	PUNCT
ap-9258	246	13	.	.	PUNCT
ap-9258	247	1	√	√	VERB
ap-9258	247	2	3ax	3ax	ADJ
ap-9258	247	3	ax	ax	NOUN
ap-9258	247	4	=	=	PUNCT
ap-9258	247	5	ax	ax	NOUN
ap-9258	247	6	ab	ab	PROPN
ap-9258	248	1	=	=	PUNCT
ap-9258	248	2	√	√	PROPN
ap-9258	248	3	3ax	3ax	NOUN
ap-9258	249	1	+	+	CCONJ
ap-9258	250	1	√	√	ADP
ap-9258	250	2	3ax	3ax	ADJ
ap-9258	250	3	−	−	PROPN
ap-9258	250	4	x	x	SYM
ap-9258	250	5	ab	ab	PROPN
ap-9258	250	6	∴	∴	PROPN
ap-9258	250	7	ab	ab	PROPN
ap-9258	250	8	=	=	PUNCT
ap-9258	250	9	2ax	2ax	ADJ
ap-9258	250	10	−	−	PROPN
ap-9258	250	11	1√	1√	PROPN
ap-9258	250	12	3	3	NUM
ap-9258	250	13	x	x	NOUN
ap-9258	250	14	,	,	PUNCT
ap-9258	250	15	(	(	PUNCT
ap-9258	250	16	41	41	NUM
ap-9258	250	17	)	)	PUNCT
ap-9258	250	18	477	477	NUM
ap-9258	250	19	t.	t.	NOUN
ap-9258	250	20	a.	a.	PROPN
ap-9258	250	21	yusuf	yusuf	PROPN
ap-9258	250	22	,	,	PUNCT
ap-9258	250	23	s.	s.	PROPN
ap-9258	250	24	a.	a.	PROPN
ap-9258	250	25	aodu	aodu	PROPN
ap-9258	250	26	,	,	PUNCT
ap-9258	250	27	a.	a.	NOUN
ap-9258	250	28	o.	o.	NOUN
ap-9258	250	29	alabi	alabi	PROPN
ap-9258	250	30	acta	acta	PROPN
ap-9258	250	31	polytechnica	polytechnica	PROPN
ap-9258	251	1	y	y	PROPN
ap-9258	251	2	x	x	PROPN
ap-9258	251	3	c	c	PROPN
ap-9258	251	4	a	a	DET
ap-9258	251	5	b	b	PROPN
ap-9258	251	6	ap	ap	PROPN
ap-9258	251	7	54o	54o	NOUN
ap-9258	251	8	72o	72o	NOUN
ap-9258	251	9	(	(	PUNCT
ap-9258	251	10	a	a	NOUN
ap-9258	251	11	)	)	PUNCT
ap-9258	251	12	.	.	PUNCT
ap-9258	252	1	surface	surface	NOUN
ap-9258	252	2	analysis	analysis	NOUN
ap-9258	252	3	.	.	PUNCT
ap-9258	253	1	x	x	X
ap-9258	253	2	c	c	NOUN
ap-9258	253	3	a	a	DET
ap-9258	253	4	θ	θ	NOUN
ap-9258	253	5	q	q	X
ap-9258	253	6	p	p	NOUN
ap-9258	253	7	r	r	NOUN
ap-9258	253	8	r	r	NOUN
ap-9258	253	9	z	z	NOUN
ap-9258	253	10	θ	θ	NOUN
ap-9258	253	11	(	(	PUNCT
ap-9258	253	12	b	b	NOUN
ap-9258	253	13	)	)	PUNCT
ap-9258	253	14	.	.	PUNCT
ap-9258	254	1	radiation	radiation	NOUN
ap-9258	254	2	analysis	analysis	NOUN
ap-9258	254	3	.	.	PUNCT
ap-9258	255	1	figure	figure	NOUN
ap-9258	255	2	7	7	NUM
ap-9258	255	3	.	.	PUNCT
ap-9258	256	1	the	the	DET
ap-9258	256	2	geometry	geometry	NOUN
ap-9258	256	3	for	for	ADP
ap-9258	256	4	the	the	DET
ap-9258	256	5	derivation	derivation	NOUN
ap-9258	256	6	of	of	ADP
ap-9258	256	7	the	the	DET
ap-9258	256	8	directional	directional	ADJ
ap-9258	256	9	factor	factor	NOUN
ap-9258	256	10	of	of	ADP
ap-9258	256	11	a	a	DET
ap-9258	256	12	pentagonal	pentagonal	ADJ
ap-9258	256	13	acoustic	acoustic	ADJ
ap-9258	256	14	piston	piston	NOUN
ap-9258	256	15	source	source	NOUN
ap-9258	256	16	.	.	PUNCT
ap-9258	257	1	y	y	NOUN
ap-9258	257	2	x	x	PROPN
ap-9258	257	3	c	c	PROPN
ap-9258	257	4	a	a	DET
ap-9258	257	5	b	b	NOUN
ap-9258	257	6	ax60o	ax60o	X
ap-9258	257	7	60o	60o	NUM
ap-9258	258	1	(	(	PUNCT
ap-9258	258	2	a	a	X
ap-9258	258	3	)	)	PUNCT
ap-9258	258	4	.	.	PUNCT
ap-9258	259	1	surface	surface	NOUN
ap-9258	259	2	analysis	analysis	NOUN
ap-9258	259	3	.	.	PUNCT
ap-9258	260	1	x	x	X
ap-9258	260	2	c	c	NOUN
ap-9258	260	3	a	a	DET
ap-9258	260	4	θ	θ	NOUN
ap-9258	260	5	q	q	X
ap-9258	260	6	p	p	NOUN
ap-9258	260	7	r	r	NOUN
ap-9258	260	8	r	r	NOUN
ap-9258	260	9	z	z	NOUN
ap-9258	260	10	θ	θ	NOUN
ap-9258	260	11	(	(	PUNCT
ap-9258	260	12	b	b	NOUN
ap-9258	260	13	)	)	PUNCT
ap-9258	260	14	.	.	PUNCT
ap-9258	261	1	radiation	radiation	NOUN
ap-9258	261	2	analysis	analysis	NOUN
ap-9258	261	3	.	.	PUNCT
ap-9258	262	1	figure	figure	NOUN
ap-9258	262	2	8	8	NUM
ap-9258	262	3	.	.	PUNCT
ap-9258	263	1	the	the	DET
ap-9258	263	2	geometry	geometry	NOUN
ap-9258	263	3	for	for	ADP
ap-9258	263	4	the	the	DET
ap-9258	263	5	derivation	derivation	NOUN
ap-9258	263	6	of	of	ADP
ap-9258	263	7	the	the	DET
ap-9258	263	8	directional	directional	ADJ
ap-9258	263	9	factor	factor	NOUN
ap-9258	263	10	of	of	ADP
ap-9258	263	11	hexagonal	hexagonal	ADJ
ap-9258	263	12	acoustic	acoustic	ADJ
ap-9258	263	13	piston	piston	NOUN
ap-9258	263	14	source	source	NOUN
ap-9258	263	15	.	.	PUNCT
ap-9258	264	1	px	px	PROPN
ap-9258	265	1	=	=	PUNCT
ap-9258	265	2	i	i	PRON
ap-9258	265	3	a	a	DET
ap-9258	265	4	r	r	NOUN
ap-9258	265	5	ei(ωt−kr	ei(ωt−kr	NOUN
ap-9258	265	6	)	)	PUNCT
ap-9258	265	7	∫	∫	PROPN
ap-9258	266	1	√	√	NUM
ap-9258	266	2	3ax	3ax	NOUN
ap-9258	267	1	−	−	PROPN
ap-9258	267	2	√	√	PROPN
ap-9258	267	3	3ax	3ax	PROPN
ap-9258	268	1	cos	cos	PROPN
ap-9258	268	2	(	(	PUNCT
ap-9258	268	3	kx	kx	PROPN
ap-9258	268	4	sin	sin	PROPN
ap-9258	268	5	θ	θ	PROPN
ap-9258	268	6	)	)	PUNCT
ap-9258	268	7	·	·	PUNCT
ap-9258	269	1	(	(	PUNCT
ap-9258	269	2	2ax	2ax	ADJ
ap-9258	269	3	−	−	PROPN
ap-9258	269	4	1√	1√	PROPN
ap-9258	269	5	3	3	NUM
ap-9258	269	6	x	x	SYM
ap-9258	269	7	)	)	PUNCT
ap-9258	269	8	dx	dx	PROPN
ap-9258	269	9	(	(	PUNCT
ap-9258	269	10	42	42	NUM
ap-9258	269	11	)	)	PUNCT
ap-9258	270	1	=	=	NOUN
ap-9258	270	2	i	i	PRON
ap-9258	270	3	a	a	DET
ap-9258	270	4	r	r	NOUN
ap-9258	270	5	2ei(ωt−kr	2ei(ωt−kr	NUM
ap-9258	270	6	)	)	PUNCT
ap-9258	270	7	{	{	PUNCT
ap-9258	270	8	2ax	2ax	ADJ
ap-9258	270	9	(	(	PUNCT
ap-9258	270	10	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	270	11	sin	sin	NOUN
ap-9258	270	12	(	(	PUNCT
ap-9258	270	13	kx	kx	PROPN
ap-9258	270	14	sin	sin	PROPN
ap-9258	270	15	θ	θ	PROPN
ap-9258	270	16	)	)	PUNCT
ap-9258	271	1	k	k	NOUN
ap-9258	271	2	sin	sin	NOUN
ap-9258	271	3	θ	θ	PROPN
ap-9258	271	4	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	271	5	√	√	PROPN
ap-9258	271	6	3ax	3ax	NOUN
ap-9258	271	7	−	−	PROPN
ap-9258	271	8	√	√	PROPN
ap-9258	271	9	3ax	3ax	NOUN
ap-9258	271	10	)	)	PUNCT
ap-9258	272	1	−	−	PROPN
ap-9258	272	2	1√	1√	NOUN
ap-9258	272	3	3	3	NUM
ap-9258	272	4	(	(	PUNCT
ap-9258	272	5	∣∣∣∣x	∣∣∣∣x	NOUN
ap-9258	272	6	sin	sin	NOUN
ap-9258	272	7	(	(	PUNCT
ap-9258	272	8	kx	kx	PROPN
ap-9258	272	9	sin	sin	PROPN
ap-9258	272	10	θ	θ	PROPN
ap-9258	272	11	)	)	PUNCT
ap-9258	272	12	k	k	NOUN
ap-9258	272	13	sin	sin	NOUN
ap-9258	272	14	θ	θ	PROPN
ap-9258	272	15	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	272	16	√	√	PROPN
ap-9258	272	17	3ax	3ax	NOUN
ap-9258	272	18	−	−	PROPN
ap-9258	273	1	√	√	PROPN
ap-9258	273	2	3ax	3ax	NOUN
ap-9258	273	3	)	)	PUNCT
ap-9258	274	1	−	−	PROPN
ap-9258	274	2	1√	1√	NOUN
ap-9258	274	3	3	3	NUM
ap-9258	274	4	(	(	PUNCT
ap-9258	274	5	∣∣∣∣cos	∣∣∣∣cos	PROPN
ap-9258	274	6	(	(	PUNCT
ap-9258	274	7	kx	kx	PROPN
ap-9258	274	8	sin	sin	PROPN
ap-9258	274	9	θ	θ	PROPN
ap-9258	274	10	)	)	PUNCT
ap-9258	274	11	k2	k2	ADJ
ap-9258	274	12	sin2	sin2	NOUN
ap-9258	274	13	θ	θ	PROPN
ap-9258	274	14	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	274	15	√	√	PROPN
ap-9258	274	16	3ax	3ax	NOUN
ap-9258	274	17	−	−	PROPN
ap-9258	274	18	√	√	PROPN
ap-9258	274	19	3ax	3ax	NOUN
ap-9258	274	20	)	)	PUNCT
ap-9258	274	21	}	}	PUNCT
ap-9258	274	22	,	,	PUNCT
ap-9258	274	23	(	(	PUNCT
ap-9258	274	24	43	43	X
ap-9258	274	25	)	)	PUNCT
ap-9258	274	26	px	px	NOUN
ap-9258	274	27	=	=	PUNCT
ap-9258	274	28	i	i	PRON
ap-9258	274	29	a	a	DET
ap-9258	274	30	r	r	NOUN
ap-9258	274	31	ei(ωt−kr)8ax	ei(ωt−kr)8ax	NOUN
ap-9258	274	32	(	(	PUNCT
ap-9258	274	33	sin	sin	NOUN
ap-9258	274	34	(	(	PUNCT
ap-9258	274	35	k	k	NOUN
ap-9258	274	36	√	√	NUM
ap-9258	274	37	3ax	3ax	ADJ
ap-9258	274	38	sin	sin	NOUN
ap-9258	274	39	θ	θ	PROPN
ap-9258	274	40	)	)	PUNCT
ap-9258	275	1	k	k	PROPN
ap-9258	275	2	sin	sin	PROPN
ap-9258	275	3	θ	θ	NOUN
ap-9258	275	4	)	)	PUNCT
ap-9258	276	1	=	=	PUNCT
ap-9258	277	1	i	i	PRON
ap-9258	277	2	a	a	DET
ap-9258	277	3	r	r	NOUN
ap-9258	278	1	ei(ωt−kr)8	ei(ωt−kr)8	INTJ
ap-9258	278	2	√	√	PROPN
ap-9258	278	3	3ax	3ax	ADJ
ap-9258	278	4	2	2	NUM
ap-9258	278	5	sin	sin	NOUN
ap-9258	278	6	(	(	PUNCT
ap-9258	278	7	k	k	NOUN
ap-9258	278	8	√	√	NUM
ap-9258	278	9	3ax	3ax	ADJ
ap-9258	278	10	sin	sin	NOUN
ap-9258	278	11	θ	θ	NOUN
ap-9258	278	12	)	)	PUNCT
ap-9258	279	1	k	k	X
ap-9258	279	2	√	√	NUM
ap-9258	279	3	3ax	3ax	ADJ
ap-9258	279	4	sin	sin	NOUN
ap-9258	279	5	θ	θ	PROPN
ap-9258	279	6	,	,	PUNCT
ap-9258	279	7	(	(	PUNCT
ap-9258	279	8	44	44	NUM
ap-9258	279	9	)	)	PUNCT
ap-9258	279	10	hx	hx	NOUN
ap-9258	279	11	=	=	SYM
ap-9258	279	12	∣∣∣∣∣	∣∣∣∣∣	PROPN
ap-9258	279	13	sin	sin	NOUN
ap-9258	279	14	(	(	PUNCT
ap-9258	279	15	k	k	NOUN
ap-9258	279	16	√	√	NUM
ap-9258	279	17	3ax	3ax	ADJ
ap-9258	279	18	sin	sin	NOUN
ap-9258	279	19	θ	θ	NOUN
ap-9258	279	20	)	)	PUNCT
ap-9258	280	1	k	k	X
ap-9258	280	2	√	√	NUM
ap-9258	280	3	3ax	3ax	ADJ
ap-9258	280	4	sin	sin	NOUN
ap-9258	280	5	θ	θ	X
ap-9258	280	6	∣∣∣∣∣	∣∣∣∣∣	PROPN
ap-9258	280	7	=	=	SYM
ap-9258	280	8	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	280	9	sin	sin	NOUN
ap-9258	280	10	(	(	PUNCT
ap-9258	280	11	kax	kax	NOUN
ap-9258	280	12	tan	tan	PROPN
ap-9258	280	13	60	60	NUM
ap-9258	280	14	sin	sin	NOUN
ap-9258	280	15	θ	θ	NOUN
ap-9258	280	16	)	)	PUNCT
ap-9258	280	17	kax	kax	NOUN
ap-9258	280	18	tan	tan	PROPN
ap-9258	280	19	60	60	NUM
ap-9258	280	20	sin	sin	NOUN
ap-9258	280	21	θ	θ	PROPN
ap-9258	280	22	∣∣∣∣.	∣∣∣∣.	PROPN
ap-9258	280	23	(	(	PUNCT
ap-9258	280	24	45	45	NUM
ap-9258	280	25	)	)	PUNCT
ap-9258	280	26	3.6	3.6	NUM
ap-9258	280	27	.	.	PUNCT
ap-9258	281	1	heptagonal	heptagonal	ADJ
ap-9258	281	2	piston	piston	NOUN
ap-9258	281	3	the	the	DET
ap-9258	281	4	centre	centre	NOUN
ap-9258	281	5	c	c	PROPN
ap-9258	281	6	of	of	ADP
ap-9258	281	7	the	the	DET
ap-9258	281	8	regular	regular	ADJ
ap-9258	281	9	heptagon	heptagon	NOUN
ap-9258	281	10	with	with	ADP
ap-9258	281	11	respect	respect	NOUN
ap-9258	281	12	to	to	ADP
ap-9258	281	13	the	the	DET
ap-9258	281	14	top	top	NOUN
ap-9258	281	15	and	and	CCONJ
ap-9258	281	16	bottom	bottom	NOUN
ap-9258	281	17	of	of	ADP
ap-9258	281	18	the	the	DET
ap-9258	281	19	non	non	ADJ
ap-9258	281	20	-	-	ADJ
ap-9258	281	21	symmetrical	symmetrical	ADJ
ap-9258	281	22	surface	surface	NOUN
ap-9258	281	23	is	be	AUX
ap-9258	281	24	as	as	SCONJ
ap-9258	281	25	shown	show	VERB
ap-9258	281	26	in	in	ADP
ap-9258	281	27	figure	figure	NOUN
ap-9258	281	28	9	9	NUM
ap-9258	281	29	.	.	PUNCT
ap-9258	282	1	by	by	ADP
ap-9258	282	2	the	the	DET
ap-9258	282	3	similar	similar	ADJ
ap-9258	282	4	triangle	triangle	NOUN
ap-9258	282	5	principle	principle	NOUN
ap-9258	282	6	,	,	PUNCT
ap-9258	282	7	the	the	DET
ap-9258	282	8	hsl	hsl	NOUN
ap-9258	282	9	,	,	PUNCT
ap-9258	282	10	ab	ab	PROPN
ap-9258	282	11	can	can	AUX
ap-9258	282	12	be	be	AUX
ap-9258	282	13	determined	determine	VERB
ap-9258	282	14	as	as	ADP
ap-9258	282	15	given	give	VERB
ap-9258	282	16	in	in	ADP
ap-9258	282	17	equation	equation	NOUN
ap-9258	282	18	(	(	PUNCT
ap-9258	282	19	46	46	NUM
ap-9258	282	20	)	)	PUNCT
ap-9258	282	21	478	478	NUM
ap-9258	282	22	vol	vol	NOUN
ap-9258	282	23	.	.	PUNCT
ap-9258	283	1	64	64	NUM
ap-9258	283	2	no	no	NOUN
ap-9258	283	3	.	.	PUNCT
ap-9258	284	1	5/2024	5/2024	ADJ
ap-9258	284	2	acoustic	acoustic	ADJ
ap-9258	284	3	radiation	radiation	NOUN
ap-9258	284	4	beam	beam	NOUN
ap-9258	284	5	patterns	pattern	NOUN
ap-9258	284	6	of	of	ADP
ap-9258	284	7	different	different	ADJ
ap-9258	284	8	polygonal	polygonal	NOUN
ap-9258	284	9	.	.	PUNCT
ap-9258	284	10	.	.	PUNCT
ap-9258	284	11	.	.	PUNCT
ap-9258	285	1	y	y	NOUN
ap-9258	285	2	x	x	PROPN
ap-9258	285	3	c	c	PROPN
ap-9258	285	4	a	a	DET
ap-9258	285	5	b	b	X
ap-9258	285	6	ah	ah	INTJ
ap-9258	285	7	64.3o	64.3o	NOUN
ap-9258	285	8	51.43o	51.43o	PROPN
ap-9258	285	9	(	(	PUNCT
ap-9258	285	10	a	a	NOUN
ap-9258	285	11	)	)	PUNCT
ap-9258	285	12	.	.	PUNCT
ap-9258	286	1	surface	surface	NOUN
ap-9258	286	2	analysis	analysis	NOUN
ap-9258	286	3	.	.	PUNCT
ap-9258	287	1	x	x	X
ap-9258	287	2	c	c	NOUN
ap-9258	287	3	a	a	DET
ap-9258	287	4	θ	θ	NOUN
ap-9258	287	5	q	q	X
ap-9258	287	6	p	p	NOUN
ap-9258	287	7	r	r	NOUN
ap-9258	287	8	r	r	NOUN
ap-9258	287	9	z	z	NOUN
ap-9258	287	10	θ	θ	NOUN
ap-9258	287	11	(	(	PUNCT
ap-9258	287	12	b	b	NOUN
ap-9258	287	13	)	)	PUNCT
ap-9258	287	14	.	.	PUNCT
ap-9258	288	1	radiation	radiation	NOUN
ap-9258	288	2	analysis	analysis	NOUN
ap-9258	288	3	.	.	PUNCT
ap-9258	289	1	figure	figure	NOUN
ap-9258	289	2	9	9	NUM
ap-9258	289	3	.	.	PUNCT
ap-9258	290	1	the	the	DET
ap-9258	290	2	geometry	geometry	NOUN
ap-9258	290	3	for	for	ADP
ap-9258	290	4	the	the	DET
ap-9258	290	5	derivation	derivation	NOUN
ap-9258	290	6	of	of	ADP
ap-9258	290	7	the	the	DET
ap-9258	290	8	directional	directional	ADJ
ap-9258	290	9	factor	factor	NOUN
ap-9258	290	10	of	of	ADP
ap-9258	290	11	heptagonal	heptagonal	ADJ
ap-9258	290	12	acoustic	acoustic	ADJ
ap-9258	290	13	piston	piston	NOUN
ap-9258	290	14	source	source	NOUN
ap-9258	290	15	.	.	PUNCT
ap-9258	291	1	and	and	CCONJ
ap-9258	291	2	the	the	DET
ap-9258	291	3	complex	complex	ADJ
ap-9258	291	4	part	part	NOUN
ap-9258	291	5	of	of	ADP
ap-9258	291	6	the	the	DET
ap-9258	291	7	pressure	pressure	NOUN
ap-9258	291	8	integral	integral	ADJ
ap-9258	291	9	can	can	NOUN
ap-9258	291	10	,	,	PUNCT
ap-9258	291	11	therefore	therefore	ADV
ap-9258	291	12	,	,	PUNCT
ap-9258	291	13	be	be	AUX
ap-9258	291	14	expressed	express	VERB
ap-9258	291	15	as	as	ADP
ap-9258	291	16	in	in	ADP
ap-9258	291	17	equation	equation	NOUN
ap-9258	291	18	(	(	PUNCT
ap-9258	291	19	47	47	NUM
ap-9258	291	20	)	)	PUNCT
ap-9258	291	21	.	.	PUNCT
ap-9258	292	1	as	as	SCONJ
ap-9258	292	2	can	can	AUX
ap-9258	292	3	be	be	AUX
ap-9258	292	4	clearly	clearly	ADV
ap-9258	292	5	observed	observe	VERB
ap-9258	292	6	from	from	ADP
ap-9258	292	7	these	these	DET
ap-9258	292	8	equations	equation	NOUN
ap-9258	292	9	,	,	PUNCT
ap-9258	292	10	the	the	DET
ap-9258	292	11	heptagon	heptagon	NOUN
ap-9258	292	12	indicates	indicate	VERB
ap-9258	292	13	almost	almost	ADV
ap-9258	292	14	an	an	DET
ap-9258	292	15	identical	identical	ADJ
ap-9258	292	16	geometry	geometry	NOUN
ap-9258	292	17	with	with	ADP
ap-9258	292	18	the	the	DET
ap-9258	292	19	pentagon	pentagon	PROPN
ap-9258	292	20	analysed	analyse	VERB
ap-9258	292	21	in	in	ADP
ap-9258	292	22	section	section	NOUN
ap-9258	292	23	3.4	3.4	NUM
ap-9258	292	24	.	.	PUNCT
ap-9258	293	1	thus	thus	ADV
ap-9258	293	2	,	,	PUNCT
ap-9258	293	3	without	without	ADP
ap-9258	293	4	any	any	DET
ap-9258	293	5	repetition	repetition	NOUN
ap-9258	293	6	of	of	ADP
ap-9258	293	7	the	the	DET
ap-9258	293	8	procedure	procedure	NOUN
ap-9258	293	9	,	,	PUNCT
ap-9258	293	10	it	it	PRON
ap-9258	293	11	is	be	AUX
ap-9258	293	12	easy	easy	ADJ
ap-9258	293	13	to	to	PART
ap-9258	293	14	determine	determine	VERB
ap-9258	293	15	that	that	DET
ap-9258	293	16	equation	equation	NOUN
ap-9258	293	17	(	(	PUNCT
ap-9258	293	18	47	47	NUM
ap-9258	293	19	)	)	PUNCT
ap-9258	293	20	takes	take	VERB
ap-9258	293	21	the	the	DET
ap-9258	293	22	final	final	ADJ
ap-9258	293	23	form	form	NOUN
ap-9258	293	24	of	of	ADP
ap-9258	293	25	equation	equation	NOUN
ap-9258	293	26	(	(	PUNCT
ap-9258	293	27	48	48	NUM
ap-9258	293	28	)	)	PUNCT
ap-9258	293	29	.	.	PUNCT
ap-9258	294	1	consequently	consequently	ADV
ap-9258	294	2	,	,	PUNCT
ap-9258	294	3	the	the	DET
ap-9258	294	4	directional	directional	ADJ
ap-9258	294	5	factor	factor	NOUN
ap-9258	294	6	follows	follow	VERB
ap-9258	294	7	a	a	DET
ap-9258	294	8	similar	similar	ADJ
ap-9258	294	9	pattern	pattern	NOUN
ap-9258	294	10	as	as	SCONJ
ap-9258	294	11	previously	previously	ADV
ap-9258	294	12	done	do	VERB
ap-9258	294	13	in	in	ADP
ap-9258	294	14	section	section	NOUN
ap-9258	294	15	3.4	3.4	NUM
ap-9258	294	16	,	,	PUNCT
ap-9258	294	17	and	and	CCONJ
ap-9258	294	18	therefore	therefore	ADV
ap-9258	294	19	expressed	express	VERB
ap-9258	294	20	as	as	ADP
ap-9258	294	21	equation	equation	NOUN
ap-9258	294	22	(	(	PUNCT
ap-9258	294	23	49	49	NUM
ap-9258	294	24	)	)	PUNCT
ap-9258	294	25	.	.	PUNCT
ap-9258	295	1	ah	ah	INTJ
ap-9258	295	2	tan	tan	PROPN
ap-9258	295	3	51.43	51.43	NUM
ap-9258	296	1	ah	ah	INTJ
ap-9258	297	1	=	=	NOUN
ap-9258	298	1	ah	ah	INTJ
ap-9258	298	2	tan	tan	PROPN
ap-9258	298	3	51.43	51.43	NUM
ap-9258	298	4	+	+	CCONJ
ap-9258	298	5	(	(	PUNCT
ap-9258	298	6	ah	ah	INTJ
ap-9258	298	7	tan	tan	PROPN
ap-9258	298	8	64.3	64.3	NUM
ap-9258	298	9	−	−	PROPN
ap-9258	298	10	x	x	SYM
ap-9258	298	11	)	)	PUNCT
ap-9258	298	12	ab	ab	PROPN
ap-9258	298	13	∴	∴	PROPN
ap-9258	298	14	ab	ab	PROPN
ap-9258	299	1	=	=	PUNCT
ap-9258	299	2	(	(	PUNCT
ap-9258	299	3	1	1	NUM
ap-9258	299	4	+	+	NUM
ap-9258	299	5	tan	tan	PROPN
ap-9258	299	6	64.3	64.3	NUM
ap-9258	299	7	tan	tan	PROPN
ap-9258	299	8	38.57	38.57	NUM
ap-9258	299	9	)	)	PUNCT
ap-9258	299	10	ah	ah	INTJ
ap-9258	299	11	−	−	NOUN
ap-9258	299	12	x	x	SYM
ap-9258	299	13	tan	tan	PROPN
ap-9258	299	14	38.57	38.57	NUM
ap-9258	299	15	,	,	PUNCT
ap-9258	299	16	(	(	PUNCT
ap-9258	299	17	46	46	NUM
ap-9258	299	18	)	)	PUNCT
ap-9258	299	19	ph	ph	NOUN
ap-9258	300	1	=	=	NOUN
ap-9258	300	2	i	i	PRON
ap-9258	300	3	a	a	DET
ap-9258	300	4	r	r	NOUN
ap-9258	300	5	ei(ωt−kr	ei(ωt−kr	NOUN
ap-9258	300	6	)	)	PUNCT
ap-9258	300	7	∫	∫	PROPN
ap-9258	301	1	1	1	NUM
ap-9258	301	2	cos	cos	PROPN
ap-9258	301	3	64.3	64.3	NUM
ap-9258	301	4	ah	ah	INTJ
ap-9258	301	5	−ah	−ah	PROPN
ap-9258	301	6	tan	tan	PROPN
ap-9258	301	7	64.3	64.3	NUM
ap-9258	301	8	cos	co	NOUN
ap-9258	301	9	(	(	PUNCT
ap-9258	301	10	kx	kx	PROPN
ap-9258	301	11	sin	sin	PROPN
ap-9258	301	12	θ	θ	PROPN
ap-9258	301	13	)	)	PUNCT
ap-9258	301	14	·	·	PUNCT
ap-9258	301	15	2	2	NUM
ap-9258	301	16	{	{	PUNCT
ap-9258	301	17	(	(	PUNCT
ap-9258	301	18	1	1	NUM
ap-9258	301	19	+	+	NUM
ap-9258	301	20	tan	tan	PROPN
ap-9258	301	21	64.3	64.3	NUM
ap-9258	301	22	tan	tan	PROPN
ap-9258	301	23	38.57	38.57	NUM
ap-9258	301	24	)	)	PUNCT
ap-9258	301	25	ah	ah	INTJ
ap-9258	301	26	−	−	NOUN
ap-9258	301	27	x	x	SYM
ap-9258	301	28	tan	tan	PROPN
ap-9258	301	29	38.57	38.57	NUM
ap-9258	301	30	}	}	PUNCT
ap-9258	301	31	dx	dx	PROPN
ap-9258	301	32	,	,	PUNCT
ap-9258	301	33	(	(	PUNCT
ap-9258	301	34	47	47	NUM
ap-9258	301	35	)	)	PUNCT
ap-9258	301	36	ph	ph	NOUN
ap-9258	302	1	=	=	NOUN
ap-9258	302	2	i	i	PRON
ap-9258	302	3	a	a	DET
ap-9258	302	4	r	r	NOUN
ap-9258	302	5	2ah	2ah	NOUN
ap-9258	302	6	2ei(ωt−kr	2ei(ωt−kr	NOUN
ap-9258	302	7	)	)	PUNCT
ap-9258	303	1	[	[	PUNCT
ap-9258	303	2	sec	sec	PROPN
ap-9258	303	3	64.3	64.3	NUM
ap-9258	303	4	{	{	PUNCT
ap-9258	303	5	1	1	NUM
ap-9258	303	6	+	+	NUM
ap-9258	303	7	tan	tan	PROPN
ap-9258	303	8	38.57	38.57	NUM
ap-9258	303	9	(	(	PUNCT
ap-9258	303	10	tan	tan	PROPN
ap-9258	303	11	64.3	64.3	NUM
ap-9258	303	12	−	−	PROPN
ap-9258	303	13	sec	sec	PROPN
ap-9258	303	14	64.3	64.3	NUM
ap-9258	303	15	)	)	PUNCT
ap-9258	303	16	}	}	PUNCT
ap-9258	303	17	{	{	PUNCT
ap-9258	303	18	sin	sin	NOUN
ap-9258	303	19	(	(	PUNCT
ap-9258	303	20	kah	kah	PROPN
ap-9258	303	21	sec	sec	PROPN
ap-9258	303	22	64.3	64.3	NUM
ap-9258	303	23	sin	sin	NOUN
ap-9258	303	24	θ	θ	PROPN
ap-9258	303	25	)	)	PUNCT
ap-9258	303	26	kah	kah	PROPN
ap-9258	303	27	sec	sec	PROPN
ap-9258	303	28	64.3	64.3	NUM
ap-9258	303	29	sin	sin	NOUN
ap-9258	303	30	θ	θ	NOUN
ap-9258	303	31	}	}	PUNCT
ap-9258	303	32	+	+	CCONJ
ap-9258	303	33	tan	tan	PROPN
ap-9258	303	34	64.3	64.3	NUM
ap-9258	303	35	(	(	PUNCT
ap-9258	303	36	1	1	NUM
ap-9258	303	37	+	+	SYM
ap-9258	303	38	2	2	NUM
ap-9258	303	39	tan	tan	PROPN
ap-9258	303	40	64.3	64.3	NUM
ap-9258	303	41	tan	tan	PROPN
ap-9258	303	42	38.57	38.57	NUM
ap-9258	303	43	)	)	PUNCT
ap-9258	303	44	{	{	PUNCT
ap-9258	303	45	sin	sin	NOUN
ap-9258	303	46	(	(	PUNCT
ap-9258	303	47	kah	kah	PROPN
ap-9258	303	48	tan	tan	PROPN
ap-9258	303	49	64.3	64.3	NUM
ap-9258	303	50	sin	sin	NOUN
ap-9258	303	51	θ	θ	PROPN
ap-9258	303	52	)	)	PUNCT
ap-9258	303	53	kah	kah	PROPN
ap-9258	303	54	tan	tan	PROPN
ap-9258	303	55	64.3	64.3	NUM
ap-9258	303	56	sin	sin	NOUN
ap-9258	303	57	θ	θ	NOUN
ap-9258	303	58	}	}	PUNCT
ap-9258	304	1	+	+	SCONJ
ap-9258	304	2	tan	tan	PROPN
ap-9258	304	3	38.57	38.57	NUM
ap-9258	304	4	2	2	NUM
ap-9258	304	5	[	[	PUNCT
ap-9258	304	6	sin	sin	NOUN
ap-9258	304	7	{	{	PUNCT
ap-9258	304	8	k	k	PROPN
ap-9258	304	9	(	(	PUNCT
ap-9258	304	10	sec	sec	PROPN
ap-9258	304	11	64.3+tan	64.3+tan	PROPN
ap-9258	304	12	64.3	64.3	NUM
ap-9258	304	13	2	2	NUM
ap-9258	304	14	)	)	PUNCT
ap-9258	304	15	ah	ah	INTJ
ap-9258	304	16	sin	sin	VERB
ap-9258	304	17	θ	θ	NOUN
ap-9258	304	18	}	}	PUNCT
ap-9258	304	19	k	k	PROPN
ap-9258	304	20	(	(	PUNCT
ap-9258	304	21	sec	sec	PROPN
ap-9258	304	22	64.3+tan	64.3+tan	PROPN
ap-9258	304	23	64.3	64.3	NUM
ap-9258	304	24	2	2	NUM
ap-9258	304	25	)	)	PUNCT
ap-9258	304	26	ah	ah	INTJ
ap-9258	305	1	sin	sin	VERB
ap-9258	305	2	θ	θ	X
ap-9258	305	3	·	·	PUNCT
ap-9258	305	4	sin	sin	NOUN
ap-9258	305	5	{	{	PUNCT
ap-9258	305	6	k	k	PROPN
ap-9258	305	7	(	(	PUNCT
ap-9258	305	8	sec	sec	PROPN
ap-9258	305	9	64.3−tan	64.3−tan	PROPN
ap-9258	305	10	64.3	64.3	NUM
ap-9258	305	11	2	2	NUM
ap-9258	305	12	)	)	PUNCT
ap-9258	305	13	ah	ah	INTJ
ap-9258	305	14	sin	sin	VERB
ap-9258	305	15	θ	θ	NOUN
ap-9258	305	16	}	}	PUNCT
ap-9258	305	17	k	k	PROPN
ap-9258	305	18	(	(	PUNCT
ap-9258	305	19	sec	sec	PROPN
ap-9258	305	20	64.3−tan	64.3−tan	PROPN
ap-9258	305	21	64.3	64.3	NUM
ap-9258	305	22	2	2	NUM
ap-9258	305	23	)	)	PUNCT
ap-9258	305	24	ah	ah	INTJ
ap-9258	305	25	sin	sin	VERB
ap-9258	305	26	θ	θ	PROPN
ap-9258	305	27	]	]	X
ap-9258	305	28	]	]	X
ap-9258	305	29	,	,	PUNCT
ap-9258	305	30	(	(	PUNCT
ap-9258	305	31	48	48	NUM
ap-9258	305	32	)	)	PUNCT
ap-9258	305	33	hh	hh	PROPN
ap-9258	306	1	=	=	SYM
ap-9258	306	2	∣∣∣∣∣sec	∣∣∣∣∣sec	PROPN
ap-9258	306	3	64.3	64.3	NUM
ap-9258	306	4	{	{	PUNCT
ap-9258	306	5	1	1	NUM
ap-9258	306	6	+	+	CCONJ
ap-9258	306	7	(	(	PUNCT
ap-9258	306	8	sec	sec	PROPN
ap-9258	306	9	64.3	64.3	NUM
ap-9258	306	10	−	−	PROPN
ap-9258	306	11	tan	tan	PROPN
ap-9258	306	12	64.3	64.3	NUM
ap-9258	306	13	tan	tan	PROPN
ap-9258	306	14	128.6	128.6	NUM
ap-9258	306	15	)	)	PUNCT
ap-9258	306	16	}	}	PUNCT
ap-9258	306	17	{	{	PUNCT
ap-9258	306	18	sin	sin	NOUN
ap-9258	306	19	(	(	PUNCT
ap-9258	306	20	kah	kah	PROPN
ap-9258	306	21	sec	sec	PROPN
ap-9258	306	22	64.3	64.3	NUM
ap-9258	306	23	sin	sin	NOUN
ap-9258	306	24	θ	θ	PROPN
ap-9258	306	25	)	)	PUNCT
ap-9258	306	26	kah	kah	PROPN
ap-9258	306	27	sec	sec	PROPN
ap-9258	306	28	64.3	64.3	NUM
ap-9258	306	29	sin	sin	NOUN
ap-9258	306	30	θ	θ	NOUN
ap-9258	306	31	}	}	PUNCT
ap-9258	307	1	+	+	CCONJ
ap-9258	307	2	tan3	tan3	PROPN
ap-9258	307	3	64.3	64.3	NUM
ap-9258	307	4	{	{	PUNCT
ap-9258	307	5	sin	sin	NOUN
ap-9258	307	6	(	(	PUNCT
ap-9258	307	7	kah	kah	PROPN
ap-9258	307	8	tan	tan	PROPN
ap-9258	307	9	64.3	64.3	NUM
ap-9258	307	10	sin	sin	NOUN
ap-9258	307	11	θ	θ	PROPN
ap-9258	307	12	)	)	PUNCT
ap-9258	307	13	kah	kah	PROPN
ap-9258	307	14	tan	tan	PROPN
ap-9258	307	15	64.3	64.3	NUM
ap-9258	307	16	sin	sin	NOUN
ap-9258	307	17	θ	θ	NOUN
ap-9258	307	18	}	}	PUNCT
ap-9258	307	19	−	−	PROPN
ap-9258	307	20	1	1	NUM
ap-9258	307	21	2	2	NUM
ap-9258	307	22	tan	tan	NOUN
ap-9258	307	23	128.6	128.6	NUM
ap-9258	307	24	[	[	PUNCT
ap-9258	307	25	sin	sin	NOUN
ap-9258	307	26	{	{	PUNCT
ap-9258	307	27	k	k	PROPN
ap-9258	307	28	(	(	PUNCT
ap-9258	307	29	sec	sec	PROPN
ap-9258	307	30	64.3+tan	64.3+tan	PROPN
ap-9258	307	31	64.3	64.3	NUM
ap-9258	307	32	2	2	NUM
ap-9258	307	33	)	)	PUNCT
ap-9258	307	34	ah	ah	INTJ
ap-9258	308	1	sin	sin	VERB
ap-9258	308	2	θ	θ	NOUN
ap-9258	308	3	}	}	PUNCT
ap-9258	308	4	k	k	PROPN
ap-9258	308	5	(	(	PUNCT
ap-9258	308	6	sec	sec	PROPN
ap-9258	308	7	64.3+tan	64.3+tan	PROPN
ap-9258	308	8	64.3	64.3	NUM
ap-9258	308	9	2	2	NUM
ap-9258	308	10	)	)	PUNCT
ap-9258	308	11	ah	ah	INTJ
ap-9258	309	1	sin	sin	VERB
ap-9258	309	2	θ	θ	X
ap-9258	309	3	·	·	PUNCT
ap-9258	309	4	sin	sin	NOUN
ap-9258	309	5	{	{	PUNCT
ap-9258	309	6	k	k	PROPN
ap-9258	309	7	(	(	PUNCT
ap-9258	309	8	sec	sec	PROPN
ap-9258	309	9	64.3−tan	64.3−tan	PROPN
ap-9258	309	10	64.3	64.3	NUM
ap-9258	309	11	2	2	NUM
ap-9258	309	12	)	)	PUNCT
ap-9258	309	13	ah	ah	INTJ
ap-9258	309	14	sin	sin	VERB
ap-9258	309	15	θ	θ	NOUN
ap-9258	309	16	}	}	PUNCT
ap-9258	309	17	k	k	PROPN
ap-9258	309	18	(	(	PUNCT
ap-9258	309	19	sec	sec	PROPN
ap-9258	309	20	64.3−tan	64.3−tan	PROPN
ap-9258	309	21	64.3	64.3	NUM
ap-9258	309	22	2	2	NUM
ap-9258	309	23	)	)	PUNCT
ap-9258	309	24	ah	ah	INTJ
ap-9258	309	25	sin	sin	VERB
ap-9258	309	26	θ	θ	X
ap-9258	309	27	]	]	PUNCT
ap-9258	309	28	∣∣∣∣∣.	∣∣∣∣∣.	X
ap-9258	309	29	(	(	PUNCT
ap-9258	309	30	49	49	NUM
ap-9258	309	31	)	)	PUNCT
ap-9258	309	32	3.7	3.7	NUM
ap-9258	309	33	.	.	PUNCT
ap-9258	310	1	octagonal	octagonal	ADJ
ap-9258	310	2	piston	piston	NOUN
ap-9258	310	3	figure	figure	NOUN
ap-9258	310	4	10	10	NUM
ap-9258	310	5	shows	show	VERB
ap-9258	310	6	the	the	DET
ap-9258	310	7	centre	centre	NOUN
ap-9258	310	8	c	c	PROPN
ap-9258	310	9	of	of	ADP
ap-9258	310	10	the	the	DET
ap-9258	310	11	regular	regular	ADJ
ap-9258	310	12	octagon	octagon	PROPN
ap-9258	310	13	piston	piston	PROPN
ap-9258	310	14	surface	surface	NOUN
ap-9258	310	15	with	with	ADP
ap-9258	310	16	a	a	DET
ap-9258	310	17	nearly	nearly	ADV
ap-9258	310	18	identical	identical	ADJ
ap-9258	310	19	symmetrical	symmetrical	ADJ
ap-9258	310	20	geometry	geometry	NOUN
ap-9258	310	21	to	to	ADP
ap-9258	310	22	the	the	DET
ap-9258	310	23	hexagon	hexagon	NOUN
ap-9258	310	24	.	.	PUNCT
ap-9258	311	1	following	follow	VERB
ap-9258	311	2	the	the	DET
ap-9258	311	3	same	same	ADJ
ap-9258	311	4	analytical	analytical	ADJ
ap-9258	311	5	procedures	procedure	NOUN
ap-9258	311	6	as	as	ADP
ap-9258	311	7	previously	previously	ADV
ap-9258	311	8	undertaken	undertake	VERB
ap-9258	311	9	in	in	ADP
ap-9258	311	10	section	section	NOUN
ap-9258	311	11	3.5	3.5	NUM
ap-9258	311	12	,	,	PUNCT
ap-9258	311	13	the	the	DET
ap-9258	311	14	hsl	hsl	NOUN
ap-9258	311	15	,	,	PUNCT
ap-9258	311	16	ab	ab	PROPN
ap-9258	311	17	,	,	PUNCT
ap-9258	311	18	the	the	DET
ap-9258	311	19	complex	complex	ADJ
ap-9258	311	20	pressure	pressure	NOUN
ap-9258	311	21	component	component	NOUN
ap-9258	311	22	,	,	PUNCT
ap-9258	311	23	po	po	NOUN
ap-9258	311	24	,	,	PUNCT
ap-9258	311	25	and	and	CCONJ
ap-9258	311	26	the	the	DET
ap-9258	311	27	directional	directional	ADJ
ap-9258	311	28	factor	factor	NOUN
ap-9258	311	29	are	be	AUX
ap-9258	311	30	derived	derive	VERB
ap-9258	311	31	as	as	SCONJ
ap-9258	311	32	expressed	express	VERB
ap-9258	311	33	in	in	ADP
ap-9258	311	34	equations	equation	NOUN
ap-9258	311	35	(	(	PUNCT
ap-9258	311	36	50)–(52	50)–(52	NUM
ap-9258	311	37	)	)	PUNCT
ap-9258	311	38	,	,	PUNCT
ap-9258	311	39	respectively	respectively	ADV
ap-9258	311	40	.	.	PUNCT
ap-9258	312	1	a0	a0	PROPN
ap-9258	312	2	a0	a0	PROPN
ap-9258	312	3	=	=	PROPN
ap-9258	312	4	a0	a0	PROPN
ap-9258	312	5	+	+	CCONJ
ap-9258	312	6	a0	a0	PROPN
ap-9258	312	7	(	(	PUNCT
ap-9258	312	8	1	1	NUM
ap-9258	312	9	+	+	CCONJ
ap-9258	312	10	√	√	NUM
ap-9258	312	11	2	2	NUM
ap-9258	312	12	)	)	PUNCT
ap-9258	312	13	−	−	PROPN
ap-9258	313	1	x	x	SYM
ap-9258	313	2	ab	ab	PROPN
ap-9258	313	3	∴	∴	PROPN
ap-9258	313	4	ab	ab	PROPN
ap-9258	314	1	=	=	PUNCT
ap-9258	314	2	(	(	PUNCT
ap-9258	314	3	2	2	NUM
ap-9258	314	4	+	+	CCONJ
ap-9258	314	5	√	√	NUM
ap-9258	314	6	2	2	NUM
ap-9258	314	7	)	)	PUNCT
ap-9258	314	8	ao	ao	NOUN
ap-9258	314	9	−	−	PROPN
ap-9258	315	1	x	x	SYM
ap-9258	315	2	,	,	PUNCT
ap-9258	315	3	(	(	PUNCT
ap-9258	315	4	50	50	NUM
ap-9258	315	5	)	)	PUNCT
ap-9258	315	6	479	479	NUM
ap-9258	315	7	t.	t.	PROPN
ap-9258	315	8	a.	a.	PROPN
ap-9258	315	9	yusuf	yusuf	PROPN
ap-9258	315	10	,	,	PUNCT
ap-9258	315	11	s.	s.	PROPN
ap-9258	315	12	a.	a.	PROPN
ap-9258	315	13	aodu	aodu	PROPN
ap-9258	315	14	,	,	PUNCT
ap-9258	315	15	a.	a.	NOUN
ap-9258	315	16	o.	o.	NOUN
ap-9258	315	17	alabi	alabi	PROPN
ap-9258	315	18	acta	acta	PROPN
ap-9258	315	19	polytechnica	polytechnica	PROPN
ap-9258	315	20	y	y	PROPN
ap-9258	316	1	x	x	PROPN
ap-9258	316	2	c	c	PROPN
ap-9258	316	3	a	a	DET
ap-9258	316	4	b	b	NOUN
ap-9258	316	5	ao	ao	NOUN
ap-9258	316	6	67.5o	67.5o	NUM
ap-9258	316	7	45o	45o	ADP
ap-9258	316	8	(	(	PUNCT
ap-9258	316	9	a	a	X
ap-9258	316	10	)	)	PUNCT
ap-9258	316	11	.	.	PUNCT
ap-9258	317	1	surface	surface	NOUN
ap-9258	317	2	analysis	analysis	NOUN
ap-9258	317	3	.	.	PUNCT
ap-9258	318	1	x	x	X
ap-9258	318	2	c	c	NOUN
ap-9258	318	3	a	a	DET
ap-9258	318	4	θ	θ	NOUN
ap-9258	318	5	q	q	X
ap-9258	318	6	p	p	NOUN
ap-9258	318	7	r	r	NOUN
ap-9258	318	8	r	r	NOUN
ap-9258	318	9	z	z	NOUN
ap-9258	318	10	θ	θ	NOUN
ap-9258	318	11	(	(	PUNCT
ap-9258	318	12	b	b	NOUN
ap-9258	318	13	)	)	PUNCT
ap-9258	318	14	.	.	PUNCT
ap-9258	319	1	radiation	radiation	NOUN
ap-9258	319	2	analysis	analysis	NOUN
ap-9258	319	3	.	.	PUNCT
ap-9258	320	1	figure	figure	NOUN
ap-9258	320	2	10	10	NUM
ap-9258	320	3	.	.	PUNCT
ap-9258	321	1	the	the	DET
ap-9258	321	2	geometry	geometry	NOUN
ap-9258	321	3	for	for	ADP
ap-9258	321	4	the	the	DET
ap-9258	321	5	derivation	derivation	NOUN
ap-9258	321	6	of	of	ADP
ap-9258	321	7	the	the	DET
ap-9258	321	8	directional	directional	ADJ
ap-9258	321	9	factor	factor	NOUN
ap-9258	321	10	of	of	ADP
ap-9258	321	11	octagonal	octagonal	ADJ
ap-9258	321	12	piston	piston	NOUN
ap-9258	321	13	source	source	NOUN
ap-9258	321	14	.	.	PUNCT
ap-9258	321	15	po	po	X
ap-9258	322	1	=	=	PUNCT
ap-9258	322	2	i	i	PRON
ap-9258	322	3	a	a	DET
ap-9258	322	4	r	r	NOUN
ap-9258	322	5	ei(ωt−kr	ei(ωt−kr	NOUN
ap-9258	322	6	)	)	PUNCT
ap-9258	322	7	∫	∫	PROPN
ap-9258	322	8	(	(	PUNCT
ap-9258	322	9	1	1	NUM
ap-9258	322	10	+	+	NUM
ap-9258	322	11	√	√	PROPN
ap-9258	322	12	2)a0	2)a0	NUM
ap-9258	322	13	−(1	−(1	PROPN
ap-9258	322	14	+	+	CCONJ
ap-9258	322	15	√	√	PROPN
ap-9258	322	16	2)a0	2)a0	NUM
ap-9258	322	17	cos	cos	PROPN
ap-9258	322	18	(	(	PUNCT
ap-9258	322	19	kx	kx	PROPN
ap-9258	322	20	sin	sin	PROPN
ap-9258	322	21	θ	θ	PROPN
ap-9258	322	22	)	)	PUNCT
ap-9258	322	23	·	·	PUNCT
ap-9258	322	24	2	2	NUM
ap-9258	322	25	{	{	PUNCT
ap-9258	322	26	(	(	PUNCT
ap-9258	322	27	2	2	NUM
ap-9258	322	28	+	+	CCONJ
ap-9258	322	29	√	√	NUM
ap-9258	322	30	2	2	NUM
ap-9258	322	31	)	)	PUNCT
ap-9258	322	32	ao	ao	ADP
ap-9258	322	33	−	−	PROPN
ap-9258	322	34	x	x	SYM
ap-9258	322	35	}	}	PUNCT
ap-9258	322	36	dx	dx	PROPN
ap-9258	323	1	=	=	SYM
ap-9258	323	2	i	i	PRON
ap-9258	323	3	a	a	DET
ap-9258	323	4	r	r	NOUN
ap-9258	323	5	ei(ωt−kr)4ao	ei(ωt−kr)4ao	ADJ
ap-9258	323	6	2	2	NUM
ap-9258	323	7	(	(	PUNCT
ap-9258	323	8	4	4	NUM
ap-9258	323	9	+	+	SYM
ap-9258	323	10	3	3	NUM
ap-9258	323	11	√	√	NUM
ap-9258	323	12	2	2	NUM
ap-9258	323	13	)	)	PUNCT
ap-9258	323	14	sin	sin	NOUN
ap-9258	323	15	(	(	PUNCT
ap-9258	323	16	k	k	X
ap-9258	323	17	(	(	PUNCT
ap-9258	323	18	1	1	NUM
ap-9258	323	19	+	+	CCONJ
ap-9258	323	20	√	√	NUM
ap-9258	323	21	2	2	NUM
ap-9258	323	22	)	)	PUNCT
ap-9258	323	23	a0	a0	NOUN
ap-9258	323	24	sin	sin	NOUN
ap-9258	323	25	θ	θ	PROPN
ap-9258	323	26	)	)	PUNCT
ap-9258	324	1	k	k	NOUN
ap-9258	324	2	(	(	PUNCT
ap-9258	324	3	1	1	NUM
ap-9258	324	4	+	+	CCONJ
ap-9258	324	5	√	√	NUM
ap-9258	324	6	2	2	NUM
ap-9258	324	7	)	)	PUNCT
ap-9258	324	8	a0	a0	NOUN
ap-9258	324	9	sin	sin	NOUN
ap-9258	324	10	θ	θ	PROPN
ap-9258	324	11	,	,	PUNCT
ap-9258	324	12	(	(	PUNCT
ap-9258	324	13	51	51	NUM
ap-9258	324	14	)	)	PUNCT
ap-9258	324	15	h0	h0	NOUN
ap-9258	324	16	=	=	PUNCT
ap-9258	325	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ap-9258	325	2	sin	sin	NOUN
ap-9258	325	3	(	(	PUNCT
ap-9258	325	4	k	k	X
ap-9258	325	5	(	(	PUNCT
ap-9258	325	6	1	1	NUM
ap-9258	325	7	+	+	CCONJ
ap-9258	325	8	√	√	NUM
ap-9258	325	9	2	2	NUM
ap-9258	325	10	)	)	PUNCT
ap-9258	325	11	a0	a0	NOUN
ap-9258	325	12	sin	sin	NOUN
ap-9258	325	13	θ	θ	PROPN
ap-9258	325	14	)	)	PUNCT
ap-9258	326	1	k	k	NOUN
ap-9258	326	2	(	(	PUNCT
ap-9258	326	3	1	1	NUM
ap-9258	326	4	+	+	CCONJ
ap-9258	326	5	√	√	NUM
ap-9258	326	6	2	2	NUM
ap-9258	326	7	)	)	PUNCT
ap-9258	326	8	a0	a0	NOUN
ap-9258	326	9	sin	sin	NOUN
ap-9258	326	10	θ	θ	PROPN
ap-9258	326	11	∣∣∣∣∣	∣∣∣∣∣	PROPN
ap-9258	326	12	=	=	SYM
ap-9258	326	13	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	326	14	sin	sin	NOUN
ap-9258	326	15	(	(	PUNCT
ap-9258	326	16	ka0	ka0	PROPN
ap-9258	326	17	tan	tan	PROPN
ap-9258	326	18	67.5	67.5	NUM
ap-9258	326	19	sin	sin	NOUN
ap-9258	326	20	θ	θ	NOUN
ap-9258	326	21	)	)	PUNCT
ap-9258	326	22	ka0	ka0	PROPN
ap-9258	326	23	tan	tan	PROPN
ap-9258	326	24	67.5	67.5	NUM
ap-9258	326	25	sin	sin	NOUN
ap-9258	326	26	θ	θ	PROPN
ap-9258	326	27	∣∣∣∣.	∣∣∣∣.	PROPN
ap-9258	326	28	(	(	PUNCT
ap-9258	326	29	52	52	NUM
ap-9258	326	30	)	)	PUNCT
ap-9258	326	31	3.8	3.8	NUM
ap-9258	326	32	.	.	PUNCT
ap-9258	327	1	nonagonal	nonagonal	ADJ
ap-9258	327	2	piston	piston	NOUN
ap-9258	327	3	like	like	ADP
ap-9258	327	4	the	the	DET
ap-9258	327	5	heptagon	heptagon	NOUN
ap-9258	327	6	,	,	PUNCT
ap-9258	327	7	figure	figure	VERB
ap-9258	327	8	11	11	NUM
ap-9258	327	9	clearly	clearly	ADV
ap-9258	327	10	shows	show	VERB
ap-9258	327	11	that	that	SCONJ
ap-9258	327	12	a	a	DET
ap-9258	327	13	non	non	ADJ
ap-9258	327	14	-	-	ADJ
ap-9258	327	15	symmetrical	symmetrical	ADJ
ap-9258	327	16	surface	surface	NOUN
ap-9258	327	17	geometry	geometry	NOUN
ap-9258	327	18	of	of	ADP
ap-9258	327	19	a	a	DET
ap-9258	327	20	regular	regular	ADJ
ap-9258	327	21	nonagon	nonagon	NOUN
ap-9258	327	22	,	,	PUNCT
ap-9258	327	23	which	which	PRON
ap-9258	327	24	is	be	AUX
ap-9258	327	25	closely	closely	ADV
ap-9258	327	26	similar	similar	ADJ
ap-9258	327	27	to	to	ADP
ap-9258	327	28	that	that	PRON
ap-9258	327	29	of	of	ADP
ap-9258	327	30	the	the	DET
ap-9258	327	31	pentagon	pentagon	PROPN
ap-9258	327	32	studied	study	VERB
ap-9258	327	33	in	in	ADP
ap-9258	327	34	section	section	NOUN
ap-9258	327	35	3.4	3.4	NUM
ap-9258	327	36	.	.	PUNCT
ap-9258	328	1	then	then	ADV
ap-9258	328	2	,	,	PUNCT
ap-9258	328	3	ab	ab	PROPN
ap-9258	328	4	and	and	CCONJ
ap-9258	328	5	the	the	DET
ap-9258	328	6	complex	complex	ADJ
ap-9258	328	7	pressure	pressure	NOUN
ap-9258	328	8	component	component	NOUN
ap-9258	328	9	,	,	PUNCT
ap-9258	328	10	pn	pn	PROPN
ap-9258	328	11	are	be	AUX
ap-9258	328	12	given	give	VERB
ap-9258	328	13	as	as	ADP
ap-9258	328	14	equations	equation	NOUN
ap-9258	328	15	(	(	PUNCT
ap-9258	328	16	53	53	NUM
ap-9258	328	17	)	)	PUNCT
ap-9258	328	18	and	and	CCONJ
ap-9258	328	19	(	(	PUNCT
ap-9258	328	20	54	54	NUM
ap-9258	328	21	)	)	PUNCT
ap-9258	328	22	,	,	PUNCT
ap-9258	328	23	respectively	respectively	ADV
ap-9258	328	24	.	.	PUNCT
ap-9258	329	1	hence	hence	ADV
ap-9258	329	2	,	,	PUNCT
ap-9258	329	3	it	it	PRON
ap-9258	329	4	is	be	AUX
ap-9258	329	5	easy	easy	ADJ
ap-9258	329	6	to	to	PART
ap-9258	329	7	identify	identify	VERB
ap-9258	329	8	that	that	SCONJ
ap-9258	329	9	the	the	DET
ap-9258	329	10	directional	directional	ADJ
ap-9258	329	11	factor	factor	NOUN
ap-9258	329	12	is	be	AUX
ap-9258	329	13	in	in	ADP
ap-9258	329	14	the	the	DET
ap-9258	329	15	form	form	NOUN
ap-9258	329	16	given	give	VERB
ap-9258	329	17	in	in	ADP
ap-9258	329	18	equation	equation	NOUN
ap-9258	329	19	(	(	PUNCT
ap-9258	329	20	55	55	NUM
ap-9258	329	21	)	)	PUNCT
ap-9258	329	22	.	.	PUNCT
ap-9258	330	1	ab	ab	PROPN
ap-9258	330	2	=	=	PUNCT
ap-9258	331	1	(	(	PUNCT
ap-9258	331	2	1	1	NUM
ap-9258	331	3	+	+	NUM
ap-9258	331	4	tan	tan	PROPN
ap-9258	331	5	70	70	NUM
ap-9258	331	6	tan	tan	PROPN
ap-9258	331	7	50	50	NUM
ap-9258	331	8	)	)	PUNCT
ap-9258	331	9	an	an	DET
ap-9258	331	10	−	−	NOUN
ap-9258	331	11	x	x	SYM
ap-9258	331	12	tan	tan	PROPN
ap-9258	331	13	50	50	NUM
ap-9258	331	14	,	,	PUNCT
ap-9258	331	15	(	(	PUNCT
ap-9258	331	16	53	53	NUM
ap-9258	331	17	)	)	PUNCT
ap-9258	331	18	pn	pn	NOUN
ap-9258	332	1	=	=	NOUN
ap-9258	332	2	i	i	PRON
ap-9258	332	3	a	a	DET
ap-9258	332	4	r	r	NOUN
ap-9258	332	5	2an	2an	NOUN
ap-9258	332	6	2ei(ωt−kr	2ei(ωt−kr	NOUN
ap-9258	332	7	)	)	PUNCT
ap-9258	333	1	sec	sec	PRON
ap-9258	333	2	70	70	NUM
ap-9258	333	3	{	{	PUNCT
ap-9258	333	4	1	1	NUM
ap-9258	333	5	+	+	NUM
ap-9258	333	6	tan	tan	PROPN
ap-9258	333	7	50	50	NUM
ap-9258	333	8	(	(	PUNCT
ap-9258	333	9	tan	tan	PROPN
ap-9258	333	10	70	70	NUM
ap-9258	333	11	−	−	NOUN
ap-9258	333	12	sec	sec	PROPN
ap-9258	333	13	70	70	NUM
ap-9258	333	14	)	)	PUNCT
ap-9258	333	15	}	}	PUNCT
ap-9258	333	16	{	{	PUNCT
ap-9258	333	17	sin	sin	NOUN
ap-9258	333	18	(	(	PUNCT
ap-9258	333	19	kan	kan	PROPN
ap-9258	333	20	sec	sec	PROPN
ap-9258	333	21	70	70	NUM
ap-9258	333	22	sin	sin	NOUN
ap-9258	333	23	θ	θ	NOUN
ap-9258	333	24	)	)	PUNCT
ap-9258	333	25	kan	kan	PROPN
ap-9258	333	26	sec	sec	PROPN
ap-9258	333	27	70	70	NUM
ap-9258	333	28	sin	sin	NOUN
ap-9258	333	29	θ	θ	NOUN
ap-9258	333	30	}	}	PUNCT
ap-9258	334	1	+	+	CCONJ
ap-9258	334	2	tan	tan	PROPN
ap-9258	334	3	70	70	NUM
ap-9258	334	4	(	(	PUNCT
ap-9258	334	5	1	1	NUM
ap-9258	334	6	+	+	SYM
ap-9258	334	7	2	2	NUM
ap-9258	334	8	tan	tan	NOUN
ap-9258	334	9	70	70	NUM
ap-9258	334	10	tan	tan	NOUN
ap-9258	334	11	50	50	NUM
ap-9258	334	12	)	)	PUNCT
ap-9258	334	13	{	{	PUNCT
ap-9258	334	14	sin	sin	NOUN
ap-9258	334	15	(	(	PUNCT
ap-9258	334	16	kan	kan	PROPN
ap-9258	334	17	tan	tan	PROPN
ap-9258	334	18	70	70	NUM
ap-9258	334	19	sin	sin	NOUN
ap-9258	334	20	θ	θ	NOUN
ap-9258	334	21	)	)	PUNCT
ap-9258	334	22	kan	kan	PROPN
ap-9258	334	23	tan	tan	PROPN
ap-9258	334	24	70	70	NUM
ap-9258	334	25	sin	sin	NOUN
ap-9258	334	26	θ	θ	NOUN
ap-9258	334	27	}	}	PUNCT
ap-9258	335	1	+	+	SYM
ap-9258	335	2	tan	tan	PROPN
ap-9258	335	3	50	50	NUM
ap-9258	335	4	2	2	NUM
ap-9258	335	5			NOUN
ap-9258	335	6	sin	sin	NOUN
ap-9258	335	7	{	{	PUNCT
ap-9258	335	8	k	k	X
ap-9258	335	9	(	(	PUNCT
ap-9258	335	10	sec	sec	PROPN
ap-9258	335	11	70+tan	70+tan	PROPN
ap-9258	335	12	70	70	NUM
ap-9258	335	13	)	)	PUNCT
ap-9258	335	14	2	2	NUM
ap-9258	335	15	a	a	DET
ap-9258	335	16	n	n	PRON
ap-9258	335	17	sin	sin	NOUN
ap-9258	335	18	θ	θ	NOUN
ap-9258	335	19	}	}	PUNCT
ap-9258	335	20	k	k	PROPN
ap-9258	335	21	(	(	PUNCT
ap-9258	335	22	sec	sec	PROPN
ap-9258	335	23	70+tan	70+tan	PROPN
ap-9258	335	24	70	70	NUM
ap-9258	335	25	)	)	PUNCT
ap-9258	335	26	2	2	NUM
ap-9258	335	27	a	a	DET
ap-9258	335	28	n	n	PRON
ap-9258	335	29	sin	sin	VERB
ap-9258	335	30	θ	θ	X
ap-9258	335	31	·	·	PUNCT
ap-9258	335	32	sin	sin	NOUN
ap-9258	335	33	{	{	PUNCT
ap-9258	335	34	k	k	X
ap-9258	335	35	(	(	PUNCT
ap-9258	335	36	sec	sec	PROPN
ap-9258	335	37	70−tan	70−tan	PROPN
ap-9258	335	38	70	70	NUM
ap-9258	335	39	)	)	PUNCT
ap-9258	335	40	2	2	NUM
ap-9258	335	41	a	a	PRON
ap-9258	335	42	n	n	PRON
ap-9258	335	43	sin	sin	NOUN
ap-9258	335	44	θ	θ	NOUN
ap-9258	335	45	}	}	PUNCT
ap-9258	335	46	k	k	PROPN
ap-9258	335	47	(	(	PUNCT
ap-9258	335	48	sec	sec	PROPN
ap-9258	335	49	70−tan	70−tan	PROPN
ap-9258	335	50	70	70	NUM
ap-9258	335	51	)	)	PUNCT
ap-9258	335	52	2	2	NUM
ap-9258	335	53	a	a	PRON
ap-9258	335	54	n	n	NOUN
ap-9258	335	55	sin	sin	VERB
ap-9258	335	56	θ	θ	PROPN
ap-9258	335	57			PROPN
ap-9258	335	58	,	,	PUNCT
ap-9258	335	59	(	(	PUNCT
ap-9258	335	60	54	54	NUM
ap-9258	335	61	)	)	PUNCT
ap-9258	336	1	hn	hn	PROPN
ap-9258	336	2	=	=	PUNCT
ap-9258	336	3	sec	sec	PROPN
ap-9258	336	4	70	70	NUM
ap-9258	336	5	{	{	PUNCT
ap-9258	336	6	1	1	NUM
ap-9258	336	7	+	+	CCONJ
ap-9258	336	8	(	(	PUNCT
ap-9258	336	9	sec	sec	PROPN
ap-9258	336	10	70	70	NUM
ap-9258	336	11	−	−	PROPN
ap-9258	336	12	tan	tan	PROPN
ap-9258	336	13	70	70	NUM
ap-9258	336	14	tan	tan	PROPN
ap-9258	336	15	140	140	NUM
ap-9258	336	16	)	)	PUNCT
ap-9258	336	17	}	}	PUNCT
ap-9258	336	18	{	{	PUNCT
ap-9258	336	19	sin	sin	NOUN
ap-9258	336	20	(	(	PUNCT
ap-9258	336	21	kan	kan	PROPN
ap-9258	336	22	sec	sec	PROPN
ap-9258	336	23	70	70	NUM
ap-9258	336	24	sin	sin	NOUN
ap-9258	336	25	θ	θ	NOUN
ap-9258	336	26	)	)	PUNCT
ap-9258	336	27	kan	kan	PROPN
ap-9258	336	28	sec	sec	PROPN
ap-9258	336	29	70	70	NUM
ap-9258	336	30	sin	sin	NOUN
ap-9258	336	31	θ	θ	NOUN
ap-9258	336	32	}	}	PUNCT
ap-9258	336	33	+	+	CCONJ
ap-9258	336	34	tan3	tan3	PROPN
ap-9258	336	35	70	70	NUM
ap-9258	336	36	{	{	PUNCT
ap-9258	336	37	sin	sin	NOUN
ap-9258	336	38	(	(	PUNCT
ap-9258	336	39	kan	kan	PROPN
ap-9258	336	40	tan	tan	PROPN
ap-9258	336	41	70	70	NUM
ap-9258	336	42	sin	sin	NOUN
ap-9258	336	43	θ	θ	NOUN
ap-9258	336	44	)	)	PUNCT
ap-9258	336	45	kan	kan	PROPN
ap-9258	336	46	tan	tan	PROPN
ap-9258	336	47	70	70	NUM
ap-9258	336	48	sin	sin	NOUN
ap-9258	336	49	θ	θ	NOUN
ap-9258	336	50	}	}	PUNCT
ap-9258	336	51	−	−	PROPN
ap-9258	336	52	1	1	NUM
ap-9258	336	53	2	2	NUM
ap-9258	336	54	tan	tan	NOUN
ap-9258	336	55	140	140	NUM
ap-9258	336	56	[	[	PUNCT
ap-9258	336	57	sin	sin	NOUN
ap-9258	336	58	{	{	PUNCT
ap-9258	336	59	k	k	PROPN
ap-9258	336	60	(	(	PUNCT
ap-9258	336	61	sec	sec	PROPN
ap-9258	336	62	70+tan	70+tan	PROPN
ap-9258	336	63	70	70	NUM
ap-9258	336	64	2	2	NUM
ap-9258	336	65	)	)	PUNCT
ap-9258	336	66	a	a	PRON
ap-9258	336	67	n	n	ADV
ap-9258	336	68	sin	sin	NOUN
ap-9258	336	69	θ	θ	NOUN
ap-9258	336	70	}	}	PUNCT
ap-9258	336	71	k	k	PROPN
ap-9258	336	72	(	(	PUNCT
ap-9258	336	73	sec	sec	PROPN
ap-9258	336	74	70+tan	70+tan	PROPN
ap-9258	336	75	70	70	NUM
ap-9258	336	76	2	2	NUM
ap-9258	336	77	)	)	PUNCT
ap-9258	336	78	a	a	PRON
ap-9258	336	79	n	n	ADV
ap-9258	336	80	sin	sin	NOUN
ap-9258	336	81	θ	θ	X
ap-9258	336	82	·	·	PUNCT
ap-9258	336	83	sin	sin	NOUN
ap-9258	336	84	{	{	PUNCT
ap-9258	336	85	k	k	X
ap-9258	336	86	(	(	PUNCT
ap-9258	336	87	sec	sec	PROPN
ap-9258	336	88	70−tan	70−tan	PROPN
ap-9258	336	89	70	70	NUM
ap-9258	336	90	2	2	NUM
ap-9258	336	91	)	)	PUNCT
ap-9258	336	92	a	a	PRON
ap-9258	336	93	n	n	ADV
ap-9258	337	1	sin	sin	NOUN
ap-9258	337	2	θ	θ	NOUN
ap-9258	337	3	}	}	PUNCT
ap-9258	337	4	k	k	PROPN
ap-9258	337	5	(	(	PUNCT
ap-9258	337	6	sec	sec	PROPN
ap-9258	337	7	70−tan	70−tan	PROPN
ap-9258	337	8	70	70	NUM
ap-9258	337	9	2	2	NUM
ap-9258	337	10	)	)	PUNCT
ap-9258	337	11	a	a	DET
ap-9258	337	12	n	n	ADV
ap-9258	337	13	sin	sin	NOUN
ap-9258	337	14	θ	θ	X
ap-9258	337	15	]	]	PUNCT
ap-9258	337	16	.	.	PUNCT
ap-9258	338	1	(	(	PUNCT
ap-9258	338	2	55	55	NUM
ap-9258	338	3	)	)	PUNCT
ap-9258	338	4	3.9	3.9	NUM
ap-9258	338	5	.	.	PUNCT
ap-9258	339	1	decagonal	decagonal	ADJ
ap-9258	339	2	piston	piston	NOUN
ap-9258	339	3	like	like	ADP
ap-9258	339	4	the	the	DET
ap-9258	339	5	octagon	octagon	NOUN
ap-9258	339	6	in	in	ADP
ap-9258	339	7	section	section	NOUN
ap-9258	339	8	3.7	3.7	NUM
ap-9258	339	9	,	,	PUNCT
ap-9258	339	10	figure	figure	NOUN
ap-9258	339	11	12	12	NUM
ap-9258	339	12	indicates	indicate	VERB
ap-9258	339	13	a	a	DET
ap-9258	339	14	clear	clear	ADJ
ap-9258	339	15	symmetrical	symmetrical	ADJ
ap-9258	339	16	similarity	similarity	NOUN
ap-9258	339	17	with	with	ADP
ap-9258	339	18	the	the	DET
ap-9258	339	19	hexagon	hexagon	NOUN
ap-9258	339	20	studied	study	VERB
ap-9258	339	21	in	in	ADP
ap-9258	339	22	section	section	NOUN
ap-9258	339	23	3.5	3.5	NUM
ap-9258	339	24	.	.	PUNCT
ap-9258	340	1	consequently	consequently	ADV
ap-9258	340	2	,	,	PUNCT
ap-9258	340	3	following	follow	VERB
ap-9258	340	4	similar	similar	ADJ
ap-9258	340	5	analytical	analytical	ADJ
ap-9258	340	6	procedures	procedure	NOUN
ap-9258	340	7	while	while	SCONJ
ap-9258	340	8	avoiding	avoid	VERB
ap-9258	340	9	repetitions	repetition	NOUN
ap-9258	340	10	,	,	PUNCT
ap-9258	340	11	the	the	DET
ap-9258	340	12	directional	directional	ADJ
ap-9258	340	13	factor	factor	NOUN
ap-9258	340	14	of	of	ADP
ap-9258	340	15	the	the	DET
ap-9258	340	16	octagonal	octagonal	ADJ
ap-9258	340	17	piston	piston	NOUN
ap-9258	340	18	can	can	AUX
ap-9258	340	19	be	be	AUX
ap-9258	340	20	expressed	express	VERB
ap-9258	340	21	as	as	ADP
ap-9258	340	22	:	:	PUNCT
ap-9258	340	23	hd	hd	PROPN
ap-9258	340	24	=	=	SYM
ap-9258	340	25	∣∣∣∣	∣∣∣∣	PROPN
ap-9258	340	26	sin	sin	NOUN
ap-9258	340	27	(	(	PUNCT
ap-9258	340	28	kad	kad	PROPN
ap-9258	340	29	tan	tan	PROPN
ap-9258	340	30	72	72	NUM
ap-9258	340	31	sin	sin	NOUN
ap-9258	340	32	θ	θ	NOUN
ap-9258	340	33	)	)	PUNCT
ap-9258	340	34	kad	kad	PROPN
ap-9258	340	35	tan	tan	PROPN
ap-9258	340	36	72	72	NUM
ap-9258	340	37	sin	sin	NOUN
ap-9258	340	38	θ	θ	PROPN
ap-9258	340	39	∣∣∣∣.	∣∣∣∣.	PROPN
ap-9258	340	40	(	(	PUNCT
ap-9258	340	41	56	56	NUM
ap-9258	340	42	)	)	PUNCT
ap-9258	340	43	480	480	NUM
ap-9258	340	44	vol	vol	NOUN
ap-9258	340	45	.	.	PROPN
ap-9258	341	1	64	64	NUM
ap-9258	341	2	no	no	NOUN
ap-9258	341	3	.	.	PUNCT
ap-9258	342	1	5/2024	5/2024	ADJ
ap-9258	342	2	acoustic	acoustic	ADJ
ap-9258	342	3	radiation	radiation	NOUN
ap-9258	342	4	beam	beam	NOUN
ap-9258	342	5	patterns	pattern	NOUN
ap-9258	342	6	of	of	ADP
ap-9258	342	7	different	different	ADJ
ap-9258	342	8	polygonal	polygonal	NOUN
ap-9258	342	9	.	.	PUNCT
ap-9258	342	10	.	.	PUNCT
ap-9258	342	11	.	.	PUNCT
ap-9258	343	1	y	y	NOUN
ap-9258	343	2	x	x	PROPN
ap-9258	343	3	c	c	PROPN
ap-9258	343	4	a	a	DET
ap-9258	343	5	b	b	NOUN
ap-9258	343	6	an	an	DET
ap-9258	343	7	70o	70o	NOUN
ap-9258	343	8	40o	40o	X
ap-9258	343	9	(	(	PUNCT
ap-9258	343	10	a	a	NOUN
ap-9258	343	11	)	)	PUNCT
ap-9258	343	12	.	.	PUNCT
ap-9258	344	1	surface	surface	NOUN
ap-9258	344	2	analysis	analysis	NOUN
ap-9258	344	3	.	.	PUNCT
ap-9258	345	1	x	x	X
ap-9258	345	2	c	c	NOUN
ap-9258	345	3	a	a	DET
ap-9258	345	4	θ	θ	NOUN
ap-9258	345	5	q	q	X
ap-9258	345	6	p	p	NOUN
ap-9258	345	7	r	r	NOUN
ap-9258	345	8	r	r	NOUN
ap-9258	345	9	z	z	NOUN
ap-9258	345	10	θ	θ	NOUN
ap-9258	345	11	(	(	PUNCT
ap-9258	345	12	b	b	NOUN
ap-9258	345	13	)	)	PUNCT
ap-9258	345	14	.	.	PUNCT
ap-9258	346	1	radiation	radiation	NOUN
ap-9258	346	2	analysis	analysis	NOUN
ap-9258	346	3	.	.	PUNCT
ap-9258	347	1	figure	figure	NOUN
ap-9258	347	2	11	11	NUM
ap-9258	347	3	.	.	PUNCT
ap-9258	348	1	the	the	DET
ap-9258	348	2	geometry	geometry	NOUN
ap-9258	348	3	for	for	ADP
ap-9258	348	4	the	the	DET
ap-9258	348	5	derivation	derivation	NOUN
ap-9258	348	6	of	of	ADP
ap-9258	348	7	the	the	DET
ap-9258	348	8	directional	directional	ADJ
ap-9258	348	9	factor	factor	NOUN
ap-9258	348	10	of	of	ADP
ap-9258	348	11	nonagonal	nonagonal	ADJ
ap-9258	348	12	acoustic	acoustic	ADJ
ap-9258	348	13	piston	piston	NOUN
ap-9258	348	14	source	source	NOUN
ap-9258	348	15	.	.	PUNCT
ap-9258	349	1	y	y	NOUN
ap-9258	349	2	x	x	PROPN
ap-9258	349	3	c	c	PROPN
ap-9258	349	4	a	a	DET
ap-9258	349	5	b	b	NOUN
ap-9258	349	6	ad	ad	NOUN
ap-9258	349	7	72o	72o	X
ap-9258	349	8	36o	36o	NUM
ap-9258	349	9	(	(	PUNCT
ap-9258	349	10	a	a	NOUN
ap-9258	349	11	)	)	PUNCT
ap-9258	349	12	.	.	PUNCT
ap-9258	350	1	surface	surface	NOUN
ap-9258	350	2	analysis	analysis	NOUN
ap-9258	350	3	.	.	PUNCT
ap-9258	351	1	x	x	X
ap-9258	351	2	c	c	NOUN
ap-9258	351	3	a	a	DET
ap-9258	351	4	θ	θ	NOUN
ap-9258	351	5	q	q	X
ap-9258	351	6	p	p	NOUN
ap-9258	351	7	r	r	NOUN
ap-9258	351	8	r	r	NOUN
ap-9258	351	9	z	z	NOUN
ap-9258	351	10	θ	θ	NOUN
ap-9258	351	11	(	(	PUNCT
ap-9258	351	12	b	b	NOUN
ap-9258	351	13	)	)	PUNCT
ap-9258	351	14	.	.	PUNCT
ap-9258	352	1	radiation	radiation	NOUN
ap-9258	352	2	analysis	analysis	NOUN
ap-9258	352	3	.	.	PUNCT
ap-9258	353	1	figure	figure	NOUN
ap-9258	353	2	12	12	NUM
ap-9258	353	3	.	.	PUNCT
ap-9258	354	1	the	the	DET
ap-9258	354	2	surface	surface	NOUN
ap-9258	354	3	geometry	geometry	NOUN
ap-9258	354	4	for	for	ADP
ap-9258	354	5	the	the	DET
ap-9258	354	6	derivation	derivation	NOUN
ap-9258	354	7	of	of	ADP
ap-9258	354	8	the	the	DET
ap-9258	354	9	directional	directional	ADJ
ap-9258	354	10	factor	factor	NOUN
ap-9258	354	11	of	of	ADP
ap-9258	354	12	decagonal	decagonal	ADJ
ap-9258	354	13	acoustic	acoustic	ADJ
ap-9258	354	14	piston	piston	NOUN
ap-9258	354	15	source	source	NOUN
ap-9258	354	16	.	.	PUNCT
ap-9258	355	1	4	4	X
ap-9258	355	2	.	.	X
ap-9258	355	3	the	the	DET
ap-9258	355	4	analysis	analysis	NOUN
ap-9258	355	5	and	and	CCONJ
ap-9258	355	6	characterisation	characterisation	NOUN
ap-9258	355	7	of	of	ADP
ap-9258	355	8	the	the	DET
ap-9258	355	9	beam	beam	NOUN
ap-9258	355	10	patterns	pattern	NOUN
ap-9258	355	11	for	for	ADP
ap-9258	355	12	each	each	DET
ap-9258	355	13	piston	piston	NOUN
ap-9258	355	14	surface	surface	NOUN
ap-9258	355	15	,	,	PUNCT
ap-9258	355	16	the	the	DET
ap-9258	355	17	beam	beam	NOUN
ap-9258	355	18	pattern	pattern	NOUN
ap-9258	355	19	is	be	AUX
ap-9258	355	20	determined	determine	VERB
ap-9258	355	21	using	use	VERB
ap-9258	355	22	equation	equation	NOUN
ap-9258	355	23	(	(	PUNCT
ap-9258	355	24	57	57	NUM
ap-9258	355	25	)	)	PUNCT
ap-9258	355	26	where	where	SCONJ
ap-9258	355	27	h	h	NOUN
ap-9258	355	28	is	be	AUX
ap-9258	355	29	the	the	DET
ap-9258	355	30	directional	directional	ADJ
ap-9258	355	31	factor	factor	NOUN
ap-9258	355	32	and	and	CCONJ
ap-9258	355	33	hmax	hmax	PROPN
ap-9258	355	34	is	be	AUX
ap-9258	355	35	its	its	PRON
ap-9258	355	36	maximum	maximum	ADJ
ap-9258	355	37	value	value	NOUN
ap-9258	355	38	.	.	PUNCT
ap-9258	356	1	the	the	DET
ap-9258	356	2	comparative	comparative	ADJ
ap-9258	356	3	plots	plot	NOUN
ap-9258	356	4	of	of	ADP
ap-9258	356	5	the	the	DET
ap-9258	356	6	beam	beam	NOUN
ap-9258	356	7	patterns	pattern	NOUN
ap-9258	356	8	for	for	ADP
ap-9258	356	9	all	all	DET
ap-9258	356	10	the	the	DET
ap-9258	356	11	pistons	piston	NOUN
ap-9258	356	12	calculated	calculate	VERB
ap-9258	356	13	at	at	ADP
ap-9258	356	14	different	different	ADJ
ap-9258	356	15	diameters	diameter	NOUN
ap-9258	356	16	of	of	ADP
ap-9258	356	17	the	the	DET
ap-9258	356	18	standard	standard	ADJ
ap-9258	356	19	circular	circular	ADJ
ap-9258	356	20	surface	surface	NOUN
ap-9258	356	21	using	use	VERB
ap-9258	356	22	the	the	DET
ap-9258	356	23	respective	respective	ADJ
ap-9258	356	24	directional	directional	ADJ
ap-9258	356	25	factors	factor	NOUN
ap-9258	356	26	derived	derive	VERB
ap-9258	356	27	in	in	ADP
ap-9258	356	28	section	section	NOUN
ap-9258	356	29	3	3	NUM
ap-9258	356	30	is	be	AUX
ap-9258	356	31	shown	show	VERB
ap-9258	356	32	in	in	ADP
ap-9258	356	33	figure	figure	NOUN
ap-9258	356	34	13	13	NUM
ap-9258	356	35	.	.	PUNCT
ap-9258	357	1	the	the	DET
ap-9258	357	2	circular	circular	ADJ
ap-9258	357	3	diameters	diameter	NOUN
ap-9258	357	4	range	range	VERB
ap-9258	357	5	from	from	ADP
ap-9258	357	6	0.28–3.0λ	0.28–3.0λ	NUM
ap-9258	357	7	since	since	SCONJ
ap-9258	357	8	the	the	DET
ap-9258	357	9	directivity	directivity	NOUN
ap-9258	357	10	of	of	ADP
ap-9258	357	11	a	a	DET
ap-9258	357	12	circular	circular	ADJ
ap-9258	357	13	transducer	transducer	NOUN
ap-9258	357	14	is	be	AUX
ap-9258	357	15	high	high	ADJ
ap-9258	357	16	enough	enough	ADV
ap-9258	357	17	when	when	SCONJ
ap-9258	357	18	the	the	DET
ap-9258	357	19	diameter	diameter	NOUN
ap-9258	357	20	is	be	AUX
ap-9258	357	21	greater	great	ADJ
ap-9258	357	22	than	than	ADP
ap-9258	357	23	2λ	2λ	NOUN
ap-9258	358	1	[	[	X
ap-9258	358	2	26	26	NUM
ap-9258	358	3	]	]	PUNCT
ap-9258	358	4	.	.	PUNCT
ap-9258	359	1	the	the	DET
ap-9258	359	2	quantitative	quantitative	ADJ
ap-9258	359	3	comparison	comparison	NOUN
ap-9258	359	4	of	of	ADP
ap-9258	359	5	the	the	DET
ap-9258	359	6	results	result	NOUN
ap-9258	359	7	indicating	indicate	VERB
ap-9258	359	8	the	the	DET
ap-9258	359	9	half	half	ADJ
ap-9258	359	10	-	-	PUNCT
ap-9258	359	11	power	power	NOUN
ap-9258	359	12	(	(	PUNCT
ap-9258	359	13	−3	−3	PROPN
ap-9258	359	14	db	db	PROPN
ap-9258	359	15	)	)	PUNCT
ap-9258	359	16	beam	beam	NOUN
ap-9258	359	17	width	width	NOUN
ap-9258	359	18	(	(	PUNCT
ap-9258	359	19	bw	bw	NOUN
ap-9258	359	20	)	)	PUNCT
ap-9258	359	21	of	of	ADP
ap-9258	359	22	the	the	DET
ap-9258	359	23	main	main	ADJ
ap-9258	359	24	lobe	lobe	NOUN
ap-9258	359	25	as	as	ADV
ap-9258	359	26	well	well	ADV
ap-9258	359	27	as	as	ADP
ap-9258	359	28	the	the	DET
ap-9258	359	29	side	side	NOUN
ap-9258	359	30	lobe	lobe	NOUN
ap-9258	359	31	level	level	NOUN
ap-9258	359	32	(	(	PUNCT
ap-9258	359	33	sll	sll	PROPN
ap-9258	359	34	)	)	PUNCT
ap-9258	359	35	of	of	ADP
ap-9258	359	36	the	the	DET
ap-9258	359	37	beam	beam	NOUN
ap-9258	359	38	patterns	pattern	NOUN
ap-9258	359	39	is	be	AUX
ap-9258	359	40	presented	present	VERB
ap-9258	359	41	in	in	ADP
ap-9258	359	42	table	table	NOUN
ap-9258	359	43	1	1	NUM
ap-9258	359	44	.	.	PUNCT
ap-9258	359	45	beam	beam	NOUN
ap-9258	359	46	pattern	pattern	NOUN
ap-9258	359	47	=	=	SYM
ap-9258	359	48	20	20	NUM
ap-9258	359	49	log	log	NOUN
ap-9258	359	50	∣∣∣∣	∣∣∣∣	NOUN
ap-9258	359	51	h	h	NOUN
ap-9258	359	52	hmax	hmax	VERB
ap-9258	359	53	∣∣∣∣.	∣∣∣∣.	PROPN
ap-9258	359	54	(	(	PUNCT
ap-9258	359	55	57	57	NUM
ap-9258	359	56	)	)	PUNCT
ap-9258	359	57	these	these	DET
ap-9258	359	58	results	result	NOUN
ap-9258	359	59	show	show	VERB
ap-9258	359	60	that	that	SCONJ
ap-9258	359	61	all	all	DET
ap-9258	359	62	the	the	DET
ap-9258	359	63	pistons	piston	NOUN
ap-9258	359	64	of	of	ADP
ap-9258	359	65	the	the	DET
ap-9258	359	66	same	same	ADJ
ap-9258	359	67	surface	surface	NOUN
ap-9258	359	68	area	area	NOUN
ap-9258	359	69	exhibit	exhibit	VERB
ap-9258	359	70	a	a	DET
ap-9258	359	71	similar	similar	ADJ
ap-9258	359	72	performance	performance	NOUN
ap-9258	359	73	with	with	ADP
ap-9258	359	74	a	a	DET
ap-9258	359	75	circular	circular	ADJ
ap-9258	359	76	piston	piston	NOUN
ap-9258	359	77	having	have	VERB
ap-9258	359	78	a	a	DET
ap-9258	359	79	diameter	diameter	NOUN
ap-9258	359	80	not	not	PART
ap-9258	359	81	greater	great	ADJ
ap-9258	359	82	than	than	ADP
ap-9258	359	83	0.28λ	0.28λ	PROPN
ap-9258	359	84	or	or	CCONJ
ap-9258	359	85	being	be	AUX
ap-9258	359	86	as	as	ADV
ap-9258	359	87	large	large	ADJ
ap-9258	359	88	as	as	ADP
ap-9258	359	89	0.43λ	0.43λ	NOUN
ap-9258	359	90	when	when	SCONJ
ap-9258	359	91	the	the	DET
ap-9258	359	92	triangle	triangle	NOUN
ap-9258	359	93	is	be	AUX
ap-9258	359	94	excluded	exclude	VERB
ap-9258	359	95	.	.	PUNCT
ap-9258	360	1	meanwhile	meanwhile	ADV
ap-9258	360	2	,	,	PUNCT
ap-9258	360	3	the	the	DET
ap-9258	360	4	rectangular	rectangular	ADJ
ap-9258	360	5	and	and	CCONJ
ap-9258	360	6	circular	circular	ADJ
ap-9258	360	7	pistons	piston	NOUN
ap-9258	360	8	of	of	ADP
ap-9258	360	9	equal	equal	ADJ
ap-9258	360	10	surface	surface	NOUN
ap-9258	360	11	area	area	NOUN
ap-9258	360	12	still	still	ADV
ap-9258	360	13	maintain	maintain	VERB
ap-9258	360	14	similar	similar	ADJ
ap-9258	360	15	radiation	radiation	NOUN
ap-9258	360	16	patterns	pattern	NOUN
ap-9258	360	17	as	as	ADV
ap-9258	360	18	long	long	ADV
ap-9258	360	19	as	as	SCONJ
ap-9258	360	20	the	the	DET
ap-9258	360	21	circular	circular	ADJ
ap-9258	360	22	diameter	diameter	NOUN
ap-9258	360	23	is	be	AUX
ap-9258	360	24	still	still	ADV
ap-9258	360	25	within	within	ADP
ap-9258	360	26	a	a	DET
ap-9258	360	27	half	half	ADJ
ap-9258	360	28	wavelength	wavelength	NOUN
ap-9258	360	29	.	.	PUNCT
ap-9258	361	1	above	above	ADP
ap-9258	361	2	this	this	PRON
ap-9258	361	3	,	,	PUNCT
ap-9258	361	4	the	the	DET
ap-9258	361	5	odd	odd	ADV
ap-9258	361	6	-	-	PUNCT
ap-9258	361	7	sided	sided	ADJ
ap-9258	361	8	non	non	ADJ
ap-9258	361	9	-	-	ADJ
ap-9258	361	10	symmetrical	symmetrical	ADJ
ap-9258	361	11	polygon	polygon	NOUN
ap-9258	361	12	surfaces	surface	NOUN
ap-9258	361	13	appear	appear	VERB
ap-9258	361	14	to	to	PART
ap-9258	361	15	have	have	VERB
ap-9258	361	16	a	a	DET
ap-9258	361	17	relatively	relatively	ADV
ap-9258	361	18	lower	low	ADJ
ap-9258	361	19	beam	beam	NOUN
ap-9258	361	20	width	width	NOUN
ap-9258	361	21	compared	compare	VERB
ap-9258	361	22	to	to	ADP
ap-9258	361	23	the	the	DET
ap-9258	361	24	symmetrical	symmetrical	ADJ
ap-9258	361	25	ones	one	NOUN
ap-9258	361	26	.	.	PUNCT
ap-9258	362	1	this	this	DET
ap-9258	362	2	finding	finding	NOUN
ap-9258	362	3	is	be	AUX
ap-9258	362	4	contrary	contrary	ADJ
ap-9258	362	5	to	to	ADP
ap-9258	362	6	what	what	PRON
ap-9258	362	7	is	be	AUX
ap-9258	362	8	reported	report	VERB
ap-9258	362	9	by	by	ADP
ap-9258	362	10	[	[	X
ap-9258	362	11	19	19	NUM
ap-9258	362	12	]	]	PUNCT
ap-9258	362	13	who	who	PRON
ap-9258	362	14	adopted	adopt	VERB
ap-9258	362	15	the	the	DET
ap-9258	362	16	square	square	NOUN
ap-9258	362	17	as	as	ADP
ap-9258	362	18	a	a	DET
ap-9258	362	19	rectangular	rectangular	ADJ
ap-9258	362	20	piston	piston	NOUN
ap-9258	362	21	and	and	CCONJ
ap-9258	362	22	reported	report	VERB
ap-9258	362	23	that	that	SCONJ
ap-9258	362	24	octagonal	octagonal	ADJ
ap-9258	362	25	,	,	PUNCT
ap-9258	362	26	hexagonal	hexagonal	ADJ
ap-9258	362	27	,	,	PUNCT
ap-9258	362	28	rectangular	rectangular	ADJ
ap-9258	362	29	,	,	PUNCT
ap-9258	362	30	and	and	CCONJ
ap-9258	362	31	circular	circular	ADJ
ap-9258	362	32	pistons	piston	NOUN
ap-9258	362	33	exhibit	exhibit	VERB
ap-9258	362	34	completely	completely	ADV
ap-9258	362	35	omnidirectional	omnidirectional	ADJ
ap-9258	362	36	beam	beam	NOUN
ap-9258	362	37	patterns	pattern	NOUN
ap-9258	362	38	when	when	SCONJ
ap-9258	362	39	the	the	DET
ap-9258	362	40	surface	surface	NOUN
ap-9258	362	41	area	area	NOUN
ap-9258	362	42	is	be	AUX
ap-9258	362	43	equivalent	equivalent	ADJ
ap-9258	362	44	to	to	ADP
ap-9258	362	45	the	the	DET
ap-9258	362	46	circular	circular	ADJ
ap-9258	362	47	diameter	diameter	NOUN
ap-9258	362	48	of	of	ADP
ap-9258	362	49	0.5λ	0.5λ	NOUN
ap-9258	362	50	.	.	PUNCT
ap-9258	363	1	481	481	NUM
ap-9258	363	2	t.	t.	PROPN
ap-9258	363	3	a.	a.	PROPN
ap-9258	363	4	yusuf	yusuf	PROPN
ap-9258	363	5	,	,	PUNCT
ap-9258	363	6	s.	s.	PROPN
ap-9258	363	7	a.	a.	PROPN
ap-9258	363	8	aodu	aodu	PROPN
ap-9258	363	9	,	,	PUNCT
ap-9258	363	10	a.	a.	NOUN
ap-9258	363	11	o.	o.	PROPN
ap-9258	363	12	alabi	alabi	PROPN
ap-9258	363	13	acta	acta	PROPN
ap-9258	363	14	polytechnica	polytechnica	PROPN
ap-9258	363	15	circular	circular	PROPN
ap-9258	363	16	triangular	triangular	PROPN
ap-9258	363	17	rectangular	rectangular	ADJ
ap-9258	363	18	square	square	ADJ
ap-9258	363	19	pentagonal	pentagonal	ADJ
ap-9258	363	20	hexagonal	hexagonal	ADJ
ap-9258	363	21	heptagonal	heptagonal	ADJ
ap-9258	363	22	octagonal	octagonal	ADJ
ap-9258	363	23	nonagonal	nonagonal	ADJ
ap-9258	363	24	decagonal	decagonal	NOUN
ap-9258	363	25	-90	-90	PUNCT
ap-9258	363	26	-60	-60	PUNCT
ap-9258	363	27	-30	-30	SYM
ap-9258	363	28	0	0	NUM
ap-9258	363	29	30	30	NUM
ap-9258	363	30	60	60	NUM
ap-9258	363	31	90	90	NUM
ap-9258	363	32	-	-	SYM
ap-9258	363	33	40	40	NUM
ap-9258	363	34	-30	-30	NUM
ap-9258	363	35	-20	-20	NUM
ap-9258	363	36	-10	-10	PUNCT
ap-9258	363	37	0	0	NUM
ap-9258	363	38	b	b	X
ap-9258	363	39	ea	ea	NOUN
ap-9258	363	40	m	m	PROPN
ap-9258	363	41	p	p	NOUN
ap-9258	363	42	at	at	ADP
ap-9258	363	43	te	te	PROPN
ap-9258	363	44	rn	rn	PROPN
ap-9258	363	45	(	(	PUNCT
ap-9258	363	46	db	db	PROPN
ap-9258	363	47	)	)	PUNCT
ap-9258	363	48	(	(	PUNCT
ap-9258	363	49	a	a	NOUN
ap-9258	363	50	)	)	PUNCT
ap-9258	363	51	.	.	PUNCT
ap-9258	364	1	0.28λ	0.28λ	PROPN
ap-9258	364	2	.	.	PUNCT
ap-9258	364	3	-90	-90	PUNCT
ap-9258	364	4	-60	-60	PUNCT
ap-9258	365	1	-30	-30	SYM
ap-9258	365	2	0	0	NUM
ap-9258	365	3	30	30	NUM
ap-9258	365	4	60	60	NUM
ap-9258	365	5	90	90	NUM
ap-9258	365	6	-	-	SYM
ap-9258	365	7	40	40	NUM
ap-9258	365	8	-30	-30	NUM
ap-9258	365	9	-20	-20	NUM
ap-9258	365	10	-10	-10	PUNCT
ap-9258	365	11	0	0	NUM
ap-9258	366	1	b	b	X
ap-9258	366	2	ea	ea	NOUN
ap-9258	366	3	m	m	PROPN
ap-9258	366	4	p	p	NOUN
ap-9258	366	5	at	at	ADP
ap-9258	366	6	te	te	PROPN
ap-9258	366	7	rn	rn	PROPN
ap-9258	366	8	(	(	PUNCT
ap-9258	366	9	db	db	PROPN
ap-9258	366	10	)	)	PUNCT
ap-9258	366	11	(	(	PUNCT
ap-9258	366	12	b	b	NOUN
ap-9258	366	13	)	)	PUNCT
ap-9258	366	14	.	.	PUNCT
ap-9258	367	1	0.43λ	0.43λ	NOUN
ap-9258	367	2	.	.	PUNCT
ap-9258	367	3	-90	-90	PUNCT
ap-9258	368	1	-60	-60	PUNCT
ap-9258	369	1	-30	-30	SYM
ap-9258	369	2	0	0	NUM
ap-9258	369	3	30	30	NUM
ap-9258	369	4	60	60	NUM
ap-9258	369	5	90	90	NUM
ap-9258	369	6	-	-	SYM
ap-9258	369	7	40	40	NUM
ap-9258	369	8	-30	-30	NUM
ap-9258	369	9	-20	-20	NUM
ap-9258	369	10	-10	-10	PUNCT
ap-9258	369	11	0	0	NUM
ap-9258	370	1	b	b	X
ap-9258	370	2	ea	ea	NOUN
ap-9258	370	3	m	m	PROPN
ap-9258	370	4	p	p	NOUN
ap-9258	370	5	at	at	ADP
ap-9258	370	6	te	te	PROPN
ap-9258	370	7	rn	rn	PROPN
ap-9258	370	8	(	(	PUNCT
ap-9258	370	9	db	db	PROPN
ap-9258	370	10	)	)	PUNCT
ap-9258	370	11	(	(	PUNCT
ap-9258	370	12	c	c	NOUN
ap-9258	370	13	)	)	PUNCT
ap-9258	370	14	.	.	PUNCT
ap-9258	371	1	0.5λ	0.5λ	NOUN
ap-9258	371	2	.	.	PUNCT
ap-9258	371	3	-90	-90	PUNCT
ap-9258	372	1	-60	-60	PUNCT
ap-9258	373	1	-30	-30	SYM
ap-9258	373	2	0	0	NUM
ap-9258	373	3	30	30	NUM
ap-9258	373	4	60	60	NUM
ap-9258	373	5	90	90	NUM
ap-9258	373	6	-	-	SYM
ap-9258	373	7	40	40	NUM
ap-9258	373	8	-30	-30	NUM
ap-9258	373	9	-20	-20	NUM
ap-9258	373	10	-10	-10	PUNCT
ap-9258	373	11	0	0	NUM
ap-9258	374	1	b	b	X
ap-9258	374	2	ea	ea	NOUN
ap-9258	374	3	m	m	PROPN
ap-9258	374	4	p	p	NOUN
ap-9258	374	5	at	at	ADP
ap-9258	374	6	te	te	PROPN
ap-9258	374	7	rn	rn	PROPN
ap-9258	374	8	(	(	PUNCT
ap-9258	374	9	db	db	PROPN
ap-9258	374	10	)	)	PUNCT
ap-9258	374	11	(	(	PUNCT
ap-9258	374	12	d	d	NOUN
ap-9258	374	13	)	)	PUNCT
ap-9258	374	14	.	.	PUNCT
ap-9258	375	1	1.0λ	1.0λ	NUM
ap-9258	375	2	.	.	PUNCT
ap-9258	375	3	-90	-90	PUNCT
ap-9258	376	1	-60	-60	PUNCT
ap-9258	377	1	-30	-30	SYM
ap-9258	377	2	0	0	NUM
ap-9258	377	3	30	30	NUM
ap-9258	377	4	60	60	NUM
ap-9258	377	5	90	90	NUM
ap-9258	377	6	-	-	SYM
ap-9258	377	7	40	40	NUM
ap-9258	377	8	-30	-30	NUM
ap-9258	377	9	-20	-20	NUM
ap-9258	377	10	-10	-10	PUNCT
ap-9258	377	11	0	0	NUM
ap-9258	378	1	b	b	X
ap-9258	378	2	ea	ea	NOUN
ap-9258	378	3	m	m	PROPN
ap-9258	378	4	p	p	NOUN
ap-9258	378	5	at	at	ADP
ap-9258	378	6	te	te	PROPN
ap-9258	378	7	rn	rn	PROPN
ap-9258	378	8	(	(	PUNCT
ap-9258	378	9	db	db	PROPN
ap-9258	378	10	)	)	PUNCT
ap-9258	378	11	(	(	PUNCT
ap-9258	378	12	e	e	NOUN
ap-9258	378	13	)	)	PUNCT
ap-9258	378	14	.	.	PUNCT
ap-9258	379	1	2.0λ	2.0λ	NOUN
ap-9258	379	2	.	.	PUNCT
ap-9258	379	3	-90	-90	PUNCT
ap-9258	379	4	-60	-60	PUNCT
ap-9258	379	5	-30	-30	SYM
ap-9258	379	6	0	0	NUM
ap-9258	379	7	30	30	NUM
ap-9258	379	8	60	60	NUM
ap-9258	379	9	90	90	NUM
ap-9258	379	10	-	-	SYM
ap-9258	379	11	40	40	NUM
ap-9258	379	12	-30	-30	NUM
ap-9258	379	13	-20	-20	NUM
ap-9258	379	14	-10	-10	PUNCT
ap-9258	379	15	0	0	NUM
ap-9258	379	16	b	b	X
ap-9258	379	17	ea	ea	NOUN
ap-9258	379	18	m	m	PROPN
ap-9258	379	19	p	p	NOUN
ap-9258	379	20	at	at	ADP
ap-9258	379	21	te	te	PROPN
ap-9258	379	22	rn	rn	PROPN
ap-9258	379	23	(	(	PUNCT
ap-9258	379	24	db	db	PROPN
ap-9258	379	25	)	)	PUNCT
ap-9258	379	26	(	(	PUNCT
ap-9258	379	27	f	f	X
ap-9258	379	28	)	)	PUNCT
ap-9258	379	29	.	.	PUNCT
ap-9258	380	1	3.0λ	3.0λ	X
ap-9258	380	2	.	.	PUNCT
ap-9258	381	1	figure	figure	NOUN
ap-9258	381	2	13	13	NUM
ap-9258	381	3	.	.	PUNCT
ap-9258	382	1	the	the	DET
ap-9258	382	2	beam	beam	NOUN
ap-9258	382	3	pattern	pattern	NOUN
ap-9258	382	4	of	of	ADP
ap-9258	382	5	polygonal	polygonal	ADJ
ap-9258	382	6	piston	piston	NOUN
ap-9258	382	7	surfaces	surface	NOUN
ap-9258	382	8	of	of	ADP
ap-9258	382	9	equal	equal	ADJ
ap-9258	382	10	surface	surface	NOUN
ap-9258	382	11	area	area	NOUN
ap-9258	382	12	with	with	ADP
ap-9258	382	13	a	a	DET
ap-9258	382	14	circular	circular	ADJ
ap-9258	382	15	piston	piston	NOUN
ap-9258	382	16	of	of	ADP
ap-9258	382	17	different	different	ADJ
ap-9258	382	18	diameters	diameter	NOUN
ap-9258	382	19	.	.	PUNCT
ap-9258	383	1	piston	piston	NOUN
ap-9258	383	2	sources	source	NOUN
ap-9258	383	3	the	the	DET
ap-9258	383	4	diameter	diameter	NOUN
ap-9258	383	5	of	of	ADP
ap-9258	383	6	the	the	DET
ap-9258	383	7	circular	circular	ADJ
ap-9258	383	8	piston	piston	NOUN
ap-9258	383	9	0.28λ	0.28λ	NOUN
ap-9258	383	10	0.43λ	0.43λ	NOUN
ap-9258	383	11	0.5λ	0.5λ	NOUN
ap-9258	383	12	1.0λ	1.0λ	NUM
ap-9258	383	13	2.0λ	2.0λ	NUM
ap-9258	383	14	3.0λ	3.0λ	NUM
ap-9258	383	15	bw	bw	NOUN
ap-9258	384	1	[	[	X
ap-9258	384	2	°	°	X
ap-9258	384	3	]	]	X
ap-9258	384	4	bw	bw	NOUN
ap-9258	385	1	[	[	X
ap-9258	385	2	°	°	X
ap-9258	385	3	]	]	X
ap-9258	385	4	bw	bw	NOUN
ap-9258	386	1	[	[	X
ap-9258	386	2	°	°	X
ap-9258	386	3	]	]	X
ap-9258	386	4	bw	bw	NOUN
ap-9258	386	5	[	[	X
ap-9258	386	6	°	°	X
ap-9258	386	7	]	]	X
ap-9258	386	8	sll	sll	PROPN
ap-9258	387	1	[	[	X
ap-9258	387	2	db	db	X
ap-9258	387	3	]	]	X
ap-9258	387	4	bw	bw	NOUN
ap-9258	388	1	[	[	X
ap-9258	388	2	°	°	X
ap-9258	388	3	]	]	X
ap-9258	388	4	sll	sll	PROPN
ap-9258	389	1	[	[	X
ap-9258	389	2	db	db	X
ap-9258	389	3	]	]	X
ap-9258	389	4	bw	bw	NOUN
ap-9258	390	1	[	[	X
ap-9258	390	2	°	°	X
ap-9258	390	3	]	]	X
ap-9258	390	4	sll	sll	PROPN
ap-9258	391	1	[	[	X
ap-9258	391	2	db	db	X
ap-9258	391	3	]	]	X
ap-9258	391	4	circular	circular	NOUN
ap-9258	391	5	180	180	NUM
ap-9258	391	6	180	180	NUM
ap-9258	391	7	180	180	NUM
ap-9258	391	8	61.9	61.9	NUM
ap-9258	391	9	29.8	29.8	NUM
ap-9258	391	10	−17.6	−17.6	NOUN
ap-9258	391	11	19.8	19.8	NUM
ap-9258	391	12	−17.5	−17.5	NOUN
ap-9258	391	13	triangular	triangular	NOUN
ap-9258	391	14	180	180	NUM
ap-9258	391	15	84.3	84.3	NUM
ap-9258	391	16	70.5	70.5	NUM
ap-9258	391	17	33.6	33.6	NUM
ap-9258	391	18	−15.1	−15.1	ADV
ap-9258	391	19	16.7	16.7	NUM
ap-9258	391	20	−15.1	−15.1	DET
ap-9258	391	21	11.1	11.1	NUM
ap-9258	391	22	−15.1	−15.1	NOUN
ap-9258	391	23	rectangular	rectangular	ADJ
ap-9258	391	24	180	180	NUM
ap-9258	391	25	180	180	NUM
ap-9258	391	26	180	180	NUM
ap-9258	391	27	68.6	68.6	NUM
ap-9258	391	28	32.7	32.7	NUM
ap-9258	391	29	−13.3	−13.3	DET
ap-9258	391	30	21.7	21.7	NUM
ap-9258	391	31	−13.2	−13.2	NOUN
ap-9258	391	32	square	square	VERB
ap-9258	391	33	180	180	NUM
ap-9258	391	34	180	180	NUM
ap-9258	391	35	173.1	173.1	NUM
ap-9258	391	36	59.9	59.9	NUM
ap-9258	391	37	28.9	28.9	NUM
ap-9258	391	38	−13.3	−13.3	ADP
ap-9258	391	39	19.2	19.2	NUM
ap-9258	391	40	−13.2	−13.2	NOUN
ap-9258	391	41	pentagonal	pentagonal	NOUN
ap-9258	391	42	180	180	NUM
ap-9258	391	43	180	180	NUM
ap-9258	391	44	121.2	121.2	NUM
ap-9258	391	45	51.7	51.7	NUM
ap-9258	391	46	25.2	25.2	NUM
ap-9258	391	47	−14.2	−14.2	NOUN
ap-9258	391	48	16.8	16.8	NUM
ap-9258	391	49	−14.2	−14.2	NOUN
ap-9258	391	50	hexagonal	hexagonal	ADJ
ap-9258	391	51	180	180	NUM
ap-9258	391	52	180	180	NUM
ap-9258	391	53	136.5	136.5	NUM
ap-9258	391	54	55.4	55.4	NUM
ap-9258	391	55	26.9	26.9	NUM
ap-9258	391	56	−13.3	−13.3	DET
ap-9258	391	57	17.9	17.9	NUM
ap-9258	391	58	−13.2	−13.2	NOUN
ap-9258	391	59	heptagonal	heptagonal	ADJ
ap-9258	391	60	180	180	NUM
ap-9258	391	61	180	180	NUM
ap-9258	391	62	127.6	127.6	NUM
ap-9258	391	63	53.3	53.3	NUM
ap-9258	391	64	26.0	26.0	NUM
ap-9258	391	65	−13.4	−13.4	NUM
ap-9258	391	66	17.3	17.3	NUM
ap-9258	391	67	−13.4	−13.4	NUM
ap-9258	391	68	octagonal	octagonal	ADJ
ap-9258	391	69	180	180	NUM
ap-9258	391	70	180	180	NUM
ap-9258	391	71	130.6	130.6	NUM
ap-9258	391	72	54.1	54.1	NUM
ap-9258	391	73	26.3	26.3	NUM
ap-9258	391	74	−13.3	−13.3	PRON
ap-9258	391	75	17.5	17.5	NUM
ap-9258	391	76	−13.2	−13.2	NOUN
ap-9258	391	77	nonagonal	nonagonal	ADJ
ap-9258	391	78	180	180	NUM
ap-9258	391	79	180	180	NUM
ap-9258	391	80	127.5	127.5	NUM
ap-9258	391	81	53.3	53.3	NUM
ap-9258	391	82	26.0	26.0	NUM
ap-9258	391	83	−13.3	−13.3	ADP
ap-9258	391	84	17.3	17.3	NUM
ap-9258	391	85	−13.3	−13.3	PRON
ap-9258	391	86	decagonal	decagonal	NOUN
ap-9258	391	87	180	180	NUM
ap-9258	391	88	180	180	NUM
ap-9258	391	89	128.2	128.2	NUM
ap-9258	391	90	53.5	53.5	NUM
ap-9258	391	91	26.1	26.1	NUM
ap-9258	391	92	−13.3	−13.3	ADP
ap-9258	391	93	17.3	17.3	NUM
ap-9258	391	94	−13.2	−13.2	NOUN
ap-9258	391	95	table	table	NOUN
ap-9258	391	96	1	1	NUM
ap-9258	391	97	.	.	PUNCT
ap-9258	392	1	the	the	DET
ap-9258	392	2	−3	−3	PROPN
ap-9258	392	3	db	db	PROPN
ap-9258	392	4	beam	beam	NOUN
ap-9258	392	5	pattern	pattern	NOUN
ap-9258	392	6	of	of	ADP
ap-9258	392	7	the	the	DET
ap-9258	392	8	polygonal	polygonal	ADJ
ap-9258	392	9	pistons	piston	NOUN
ap-9258	392	10	of	of	ADP
ap-9258	392	11	the	the	DET
ap-9258	392	12	same	same	ADJ
ap-9258	392	13	surface	surface	NOUN
ap-9258	392	14	area	area	NOUN
ap-9258	392	15	with	with	ADP
ap-9258	392	16	a	a	DET
ap-9258	392	17	circular	circular	ADJ
ap-9258	392	18	piston	piston	NOUN
ap-9258	392	19	of	of	ADP
ap-9258	392	20	different	different	ADJ
ap-9258	392	21	diameters	diameter	NOUN
ap-9258	392	22	.	.	PUNCT
ap-9258	393	1	meanwhile	meanwhile	ADV
ap-9258	393	2	,	,	PUNCT
ap-9258	393	3	the	the	DET
ap-9258	393	4	circular	circular	ADJ
ap-9258	393	5	piston	piston	NOUN
ap-9258	393	6	is	be	AUX
ap-9258	393	7	better	well	ADJ
ap-9258	393	8	than	than	ADP
ap-9258	393	9	all	all	DET
ap-9258	393	10	the	the	DET
ap-9258	393	11	polygons	polygon	NOUN
ap-9258	393	12	in	in	ADP
ap-9258	393	13	terms	term	NOUN
ap-9258	393	14	of	of	ADP
ap-9258	393	15	its	its	PRON
ap-9258	393	16	side	side	NOUN
ap-9258	393	17	lobe	lobe	NOUN
ap-9258	393	18	level	level	NOUN
ap-9258	393	19	.	.	PUNCT
ap-9258	394	1	however	however	ADV
ap-9258	394	2	,	,	PUNCT
ap-9258	394	3	it	it	PRON
ap-9258	394	4	is	be	AUX
ap-9258	394	5	worse	bad	ADJ
ap-9258	394	6	in	in	ADP
ap-9258	394	7	terms	term	NOUN
ap-9258	394	8	of	of	ADP
ap-9258	394	9	its	its	PRON
ap-9258	394	10	beam	beam	NOUN
ap-9258	394	11	width	width	NOUN
ap-9258	394	12	compared	compare	VERB
ap-9258	394	13	to	to	ADP
ap-9258	394	14	the	the	DET
ap-9258	394	15	rectangular	rectangular	ADJ
ap-9258	394	16	piston	piston	NOUN
ap-9258	394	17	and	and	CCONJ
ap-9258	394	18	not	not	PART
ap-9258	394	19	much	much	ADV
ap-9258	394	20	significantly	significantly	ADV
ap-9258	394	21	different	different	ADJ
ap-9258	394	22	from	from	ADP
ap-9258	394	23	the	the	DET
ap-9258	394	24	square	square	NOUN
ap-9258	394	25	.	.	PUNCT
ap-9258	395	1	coincidentally	coincidentally	ADV
ap-9258	395	2	,	,	PUNCT
ap-9258	395	3	the	the	DET
ap-9258	395	4	closeness	closeness	NOUN
ap-9258	395	5	observed	observe	VERB
ap-9258	395	6	in	in	ADP
ap-9258	395	7	the	the	DET
ap-9258	395	8	radiation	radiation	NOUN
ap-9258	395	9	beam	beam	NOUN
ap-9258	395	10	patterns	pattern	NOUN
ap-9258	395	11	between	between	ADP
ap-9258	395	12	the	the	DET
ap-9258	395	13	square	square	ADJ
ap-9258	395	14	and	and	CCONJ
ap-9258	395	15	circular	circular	ADJ
ap-9258	395	16	pistons	piston	NOUN
ap-9258	395	17	had	have	AUX
ap-9258	395	18	equally	equally	ADV
ap-9258	395	19	been	be	AUX
ap-9258	395	20	reported	report	VERB
ap-9258	395	21	for	for	ADP
ap-9258	395	22	their	their	PRON
ap-9258	395	23	radiation	radiation	NOUN
ap-9258	395	24	impedances	impedance	NOUN
ap-9258	395	25	[	[	X
ap-9258	395	26	27	27	NUM
ap-9258	395	27	]	]	PUNCT
ap-9258	395	28	.	.	PUNCT
ap-9258	396	1	the	the	DET
ap-9258	396	2	side	side	NOUN
ap-9258	396	3	lobe	lobe	PROPN
ap-9258	396	4	levels	level	NOUN
ap-9258	396	5	remain	remain	VERB
ap-9258	396	6	the	the	DET
ap-9258	396	7	same	same	ADJ
ap-9258	396	8	at	at	ADP
ap-9258	396	9	less	less	ADJ
ap-9258	396	10	than	than	SCONJ
ap-9258	396	11	−13	−13	NOUN
ap-9258	396	12	db	db	VERB
ap-9258	396	13	for	for	ADP
ap-9258	396	14	all	all	DET
ap-9258	396	15	other	other	ADJ
ap-9258	396	16	polygons	polygon	NOUN
ap-9258	396	17	but	but	CCONJ
ap-9258	396	18	lower	low	ADJ
ap-9258	396	19	than	than	ADP
ap-9258	396	20	−14	−14	NUM
ap-9258	396	21	db	db	PROPN
ap-9258	396	22	for	for	ADP
ap-9258	396	23	the	the	DET
ap-9258	396	24	triangular	triangular	NOUN
ap-9258	396	25	and	and	CCONJ
ap-9258	396	26	pentagonal	pentagonal	ADJ
ap-9258	396	27	pistons	piston	NOUN
ap-9258	396	28	.	.	PUNCT
ap-9258	397	1	notably	notably	ADV
ap-9258	397	2	,	,	PUNCT
ap-9258	397	3	the	the	DET
ap-9258	397	4	radiation	radiation	NOUN
ap-9258	397	5	pattern	pattern	NOUN
ap-9258	397	6	of	of	ADP
ap-9258	397	7	the	the	DET
ap-9258	397	8	triangular	triangular	NOUN
ap-9258	397	9	piston	piston	NOUN
ap-9258	397	10	is	be	AUX
ap-9258	397	11	completely	completely	ADV
ap-9258	397	12	unique	unique	ADJ
ap-9258	397	13	from	from	ADP
ap-9258	397	14	other	other	ADJ
ap-9258	397	15	polygon	polygon	NOUN
ap-9258	397	16	surfaces	surface	NOUN
ap-9258	397	17	.	.	PUNCT
ap-9258	398	1	it	it	PRON
ap-9258	398	2	has	have	VERB
ap-9258	398	3	482	482	NUM
ap-9258	398	4	vol	vol	NOUN
ap-9258	398	5	.	.	PUNCT
ap-9258	399	1	64	64	NUM
ap-9258	399	2	no	no	NOUN
ap-9258	399	3	.	.	PUNCT
ap-9258	400	1	5/2024	5/2024	ADJ
ap-9258	400	2	acoustic	acoustic	ADJ
ap-9258	400	3	radiation	radiation	NOUN
ap-9258	400	4	beam	beam	NOUN
ap-9258	400	5	patterns	pattern	NOUN
ap-9258	400	6	of	of	ADP
ap-9258	400	7	different	different	ADJ
ap-9258	400	8	polygonal	polygonal	NOUN
ap-9258	400	9	.	.	PUNCT
ap-9258	400	10	.	.	PUNCT
ap-9258	400	11	.	.	PUNCT
ap-9258	401	1	a	a	DET
ap-9258	401	2	narrower	narrow	ADJ
ap-9258	401	3	beam	beam	NOUN
ap-9258	401	4	width	width	NOUN
ap-9258	401	5	,	,	PUNCT
ap-9258	401	6	one	one	NUM
ap-9258	401	7	side	side	NOUN
ap-9258	401	8	lobe	lobe	VERB
ap-9258	401	9	higher	high	ADJ
ap-9258	401	10	than	than	ADP
ap-9258	401	11	the	the	DET
ap-9258	401	12	others	other	NOUN
ap-9258	401	13	,	,	PUNCT
ap-9258	401	14	and	and	CCONJ
ap-9258	401	15	the	the	DET
ap-9258	401	16	lowest	low	ADJ
ap-9258	401	17	side	side	NOUN
ap-9258	401	18	lobe	lobe	ADJ
ap-9258	401	19	level	level	NOUN
ap-9258	401	20	next	next	ADV
ap-9258	401	21	to	to	ADP
ap-9258	401	22	the	the	DET
ap-9258	401	23	circular	circular	ADJ
ap-9258	401	24	piston	piston	NOUN
ap-9258	401	25	.	.	PUNCT
ap-9258	402	1	perhaps	perhaps	ADV
ap-9258	402	2	,	,	PUNCT
ap-9258	402	3	this	this	PRON
ap-9258	402	4	explains	explain	VERB
ap-9258	402	5	why	why	SCONJ
ap-9258	402	6	it	it	PRON
ap-9258	402	7	does	do	AUX
ap-9258	402	8	not	not	PART
ap-9258	402	9	appear	appear	VERB
ap-9258	402	10	to	to	PART
ap-9258	402	11	have	have	VERB
ap-9258	402	12	any	any	DET
ap-9258	402	13	practical	practical	ADJ
ap-9258	402	14	application	application	NOUN
ap-9258	402	15	,	,	PUNCT
ap-9258	402	16	nor	nor	CCONJ
ap-9258	402	17	is	be	AUX
ap-9258	402	18	it	it	PRON
ap-9258	402	19	well	well	ADV
ap-9258	402	20	known	know	VERB
ap-9258	402	21	in	in	ADP
ap-9258	402	22	the	the	DET
ap-9258	402	23	literature	literature	NOUN
ap-9258	402	24	[	[	X
ap-9258	402	25	28	28	NUM
ap-9258	402	26	]	]	PUNCT
ap-9258	402	27	.	.	PUNCT
ap-9258	403	1	for	for	ADP
ap-9258	403	2	the	the	DET
ap-9258	403	3	number	number	NOUN
ap-9258	403	4	of	of	ADP
ap-9258	403	5	sides	side	NOUN
ap-9258	403	6	higher	high	ADJ
ap-9258	403	7	than	than	ADP
ap-9258	403	8	five	five	NUM
ap-9258	403	9	,	,	PUNCT
ap-9258	403	10	the	the	DET
ap-9258	403	11	radiation	radiation	NOUN
ap-9258	403	12	beam	beam	NOUN
ap-9258	403	13	characteristics	characteristic	NOUN
ap-9258	403	14	are	be	AUX
ap-9258	403	15	almost	almost	ADV
ap-9258	403	16	identical	identical	ADJ
ap-9258	403	17	for	for	ADP
ap-9258	403	18	all	all	DET
ap-9258	403	19	the	the	DET
ap-9258	403	20	polygons	polygon	NOUN
ap-9258	403	21	.	.	PUNCT
ap-9258	404	1	nevertheless	nevertheless	ADV
ap-9258	404	2	,	,	PUNCT
ap-9258	404	3	the	the	DET
ap-9258	404	4	hexagonal	hexagonal	ADJ
ap-9258	404	5	piston	piston	NOUN
ap-9258	404	6	seems	seem	VERB
ap-9258	404	7	to	to	PART
ap-9258	404	8	be	be	AUX
ap-9258	404	9	the	the	DET
ap-9258	404	10	best	good	ADJ
ap-9258	404	11	while	while	NOUN
ap-9258	404	12	heptagonal	heptagonal	ADJ
ap-9258	404	13	,	,	PUNCT
ap-9258	404	14	nonagonal	nonagonal	ADJ
ap-9258	404	15	,	,	PUNCT
ap-9258	404	16	and	and	CCONJ
ap-9258	404	17	decagonal	decagonal	ADJ
ap-9258	404	18	ones	one	NOUN
ap-9258	404	19	are	be	AUX
ap-9258	404	20	generally	generally	ADV
ap-9258	404	21	the	the	DET
ap-9258	404	22	same	same	ADJ
ap-9258	404	23	.	.	PUNCT
ap-9258	405	1	one	one	PRON
ap-9258	405	2	would	would	AUX
ap-9258	405	3	expect	expect	VERB
ap-9258	405	4	that	that	SCONJ
ap-9258	405	5	the	the	DET
ap-9258	405	6	performance	performance	NOUN
ap-9258	405	7	characteristics	characteristic	NOUN
ap-9258	405	8	of	of	ADP
ap-9258	405	9	the	the	DET
ap-9258	405	10	acoustic	acoustic	ADJ
ap-9258	405	11	polygonal	polygonal	ADJ
ap-9258	405	12	pistons	piston	NOUN
ap-9258	405	13	become	become	VERB
ap-9258	405	14	closer	close	ADJ
ap-9258	405	15	to	to	ADP
ap-9258	405	16	the	the	DET
ap-9258	405	17	circular	circular	ADJ
ap-9258	405	18	piston	piston	NOUN
ap-9258	405	19	as	as	ADP
ap-9258	405	20	the	the	DET
ap-9258	405	21	number	number	NOUN
ap-9258	405	22	of	of	ADP
ap-9258	405	23	sides	side	NOUN
ap-9258	405	24	increases	increase	VERB
ap-9258	405	25	.	.	PUNCT
ap-9258	406	1	however	however	ADV
ap-9258	406	2	,	,	PUNCT
ap-9258	406	3	this	this	DET
ap-9258	406	4	result	result	NOUN
ap-9258	406	5	has	have	AUX
ap-9258	406	6	shown	show	VERB
ap-9258	406	7	that	that	SCONJ
ap-9258	406	8	neither	neither	CCONJ
ap-9258	406	9	the	the	DET
ap-9258	406	10	surface	surface	NOUN
ap-9258	406	11	area	area	NOUN
ap-9258	406	12	nor	nor	CCONJ
ap-9258	406	13	the	the	DET
ap-9258	406	14	number	number	NOUN
ap-9258	406	15	of	of	ADP
ap-9258	406	16	sides	side	NOUN
ap-9258	406	17	of	of	ADP
ap-9258	406	18	the	the	DET
ap-9258	406	19	polygon	polygon	NOUN
ap-9258	406	20	influences	influence	VERB
ap-9258	406	21	the	the	DET
ap-9258	406	22	radiation	radiation	NOUN
ap-9258	406	23	pattern	pattern	NOUN
ap-9258	406	24	.	.	PUNCT
ap-9258	407	1	rather	rather	ADV
ap-9258	407	2	,	,	PUNCT
ap-9258	407	3	it	it	PRON
ap-9258	407	4	is	be	AUX
ap-9258	407	5	the	the	DET
ap-9258	407	6	combination	combination	NOUN
ap-9258	407	7	of	of	ADP
ap-9258	407	8	the	the	DET
ap-9258	407	9	perimeter	perimeter	NOUN
ap-9258	407	10	and	and	CCONJ
ap-9258	407	11	the	the	DET
ap-9258	407	12	symmetry	symmetry	NOUN
ap-9258	407	13	of	of	ADP
ap-9258	407	14	the	the	DET
ap-9258	407	15	surface	surface	NOUN
ap-9258	407	16	.	.	PUNCT
ap-9258	408	1	at	at	ADP
ap-9258	408	2	equal	equal	ADJ
ap-9258	408	3	surface	surface	NOUN
ap-9258	408	4	area	area	NOUN
ap-9258	408	5	,	,	PUNCT
ap-9258	408	6	all	all	DET
ap-9258	408	7	the	the	DET
ap-9258	408	8	polygons	polygon	NOUN
ap-9258	408	9	are	be	AUX
ap-9258	408	10	higher	high	ADJ
ap-9258	408	11	in	in	ADP
ap-9258	408	12	perimeter	perimeter	NOUN
ap-9258	408	13	than	than	ADP
ap-9258	408	14	the	the	DET
ap-9258	408	15	circle	circle	NOUN
ap-9258	408	16	while	while	SCONJ
ap-9258	408	17	their	their	PRON
ap-9258	408	18	perimeter	perimeter	NOUN
ap-9258	408	19	decreases	decrease	VERB
ap-9258	408	20	as	as	SCONJ
ap-9258	408	21	the	the	DET
ap-9258	408	22	number	number	NOUN
ap-9258	408	23	of	of	ADP
ap-9258	408	24	sides	side	NOUN
ap-9258	408	25	increases	increase	VERB
ap-9258	408	26	in	in	ADP
ap-9258	408	27	order	order	NOUN
ap-9258	408	28	of	of	ADP
ap-9258	408	29	their	their	PRON
ap-9258	408	30	list	list	NOUN
ap-9258	408	31	in	in	ADP
ap-9258	408	32	table	table	NOUN
ap-9258	408	33	1	1	NUM
ap-9258	408	34	.	.	PUNCT
ap-9258	409	1	the	the	DET
ap-9258	409	2	triangle	triangle	NOUN
ap-9258	409	3	,	,	PUNCT
ap-9258	409	4	which	which	PRON
ap-9258	409	5	has	have	VERB
ap-9258	409	6	the	the	DET
ap-9258	409	7	highest	high	ADJ
ap-9258	409	8	perimeter	perimeter	NOUN
ap-9258	409	9	,	,	PUNCT
ap-9258	409	10	exhibits	exhibit	VERB
ap-9258	409	11	the	the	DET
ap-9258	409	12	narrowest	narrow	ADJ
ap-9258	409	13	beamwidth	beamwidth	NOUN
ap-9258	409	14	due	due	ADP
ap-9258	409	15	to	to	ADP
ap-9258	409	16	its	its	PRON
ap-9258	409	17	non	non	ADJ
ap-9258	409	18	-	-	NOUN
ap-9258	409	19	symmetry	symmetry	NOUN
ap-9258	409	20	while	while	SCONJ
ap-9258	409	21	the	the	DET
ap-9258	409	22	rectangle	rectangle	NOUN
ap-9258	409	23	and	and	CCONJ
ap-9258	409	24	square	square	ADJ
ap-9258	409	25	ones	one	NOUN
ap-9258	409	26	have	have	VERB
ap-9258	409	27	the	the	DET
ap-9258	409	28	first	first	ADJ
ap-9258	409	29	and	and	CCONJ
ap-9258	409	30	second	second	ADJ
ap-9258	409	31	overall	overall	ADJ
ap-9258	409	32	dominance	dominance	NOUN
ap-9258	409	33	.	.	PUNCT
ap-9258	410	1	consequently	consequently	ADV
ap-9258	410	2	,	,	PUNCT
ap-9258	410	3	the	the	DET
ap-9258	410	4	surface	surface	NOUN
ap-9258	410	5	symmetry	symmetry	NOUN
ap-9258	410	6	factor	factor	NOUN
ap-9258	410	7	takes	take	VERB
ap-9258	410	8	precedence	precedence	NOUN
ap-9258	410	9	over	over	ADP
ap-9258	410	10	the	the	DET
ap-9258	410	11	perimeter	perimeter	NOUN
ap-9258	410	12	such	such	ADJ
ap-9258	410	13	as	as	ADP
ap-9258	410	14	in	in	ADP
ap-9258	410	15	the	the	DET
ap-9258	410	16	case	case	NOUN
ap-9258	410	17	of	of	ADP
ap-9258	410	18	the	the	DET
ap-9258	410	19	hexagon	hexagon	NOUN
ap-9258	410	20	and	and	CCONJ
ap-9258	410	21	octagon	octagon	PROPN
ap-9258	410	22	relative	relative	ADJ
ap-9258	410	23	to	to	ADP
ap-9258	410	24	the	the	DET
ap-9258	410	25	pentagon	pentagon	PROPN
ap-9258	410	26	and	and	CCONJ
ap-9258	410	27	in	in	ADP
ap-9258	410	28	the	the	DET
ap-9258	410	29	case	case	NOUN
ap-9258	410	30	of	of	ADP
ap-9258	410	31	the	the	DET
ap-9258	410	32	last	last	ADJ
ap-9258	410	33	four	four	NUM
ap-9258	410	34	polygons	polygon	NOUN
ap-9258	410	35	relative	relative	ADJ
ap-9258	410	36	to	to	ADP
ap-9258	410	37	one	one	NUM
ap-9258	410	38	another	another	DET
ap-9258	410	39	.	.	PUNCT
ap-9258	411	1	5	5	X
ap-9258	411	2	.	.	X
ap-9258	411	3	validation	validation	NOUN
ap-9258	411	4	by	by	ADP
ap-9258	411	5	finite	finite	PROPN
ap-9258	411	6	element	element	NOUN
ap-9258	411	7	method	method	NOUN
ap-9258	411	8	to	to	PART
ap-9258	411	9	prove	prove	VERB
ap-9258	411	10	the	the	DET
ap-9258	411	11	correctness	correctness	NOUN
ap-9258	411	12	of	of	ADP
ap-9258	411	13	the	the	DET
ap-9258	411	14	directional	directional	ADJ
ap-9258	411	15	factors	factor	NOUN
ap-9258	411	16	of	of	ADP
ap-9258	411	17	each	each	DET
ap-9258	411	18	acoustic	acoustic	ADJ
ap-9258	411	19	polygonal	polygonal	ADJ
ap-9258	411	20	piston	piston	NOUN
ap-9258	411	21	source	source	NOUN
ap-9258	411	22	proposed	propose	VERB
ap-9258	411	23	in	in	ADP
ap-9258	411	24	this	this	DET
ap-9258	411	25	study	study	NOUN
ap-9258	411	26	,	,	PUNCT
ap-9258	411	27	the	the	DET
ap-9258	411	28	finite	finite	PROPN
ap-9258	411	29	element	element	NOUN
ap-9258	411	30	method	method	NOUN
ap-9258	411	31	(	(	PUNCT
ap-9258	411	32	fem	fem	PROPN
ap-9258	411	33	)	)	PUNCT
ap-9258	411	34	was	be	AUX
ap-9258	411	35	employed	employ	VERB
ap-9258	411	36	for	for	ADP
ap-9258	411	37	the	the	DET
ap-9258	411	38	validation	validation	NOUN
ap-9258	411	39	of	of	ADP
ap-9258	411	40	the	the	DET
ap-9258	411	41	radiation	radiation	NOUN
ap-9258	411	42	patterns	pattern	NOUN
ap-9258	411	43	using	use	VERB
ap-9258	411	44	the	the	DET
ap-9258	411	45	pzflex	pzflex	ADJ
ap-9258	411	46	®	®	NOUN
ap-9258	411	47	commercial	commercial	ADJ
ap-9258	411	48	software	software	NOUN
ap-9258	411	49	.	.	PUNCT
ap-9258	412	1	the	the	DET
ap-9258	412	2	first	first	ADJ
ap-9258	412	3	eight	eight	NUM
ap-9258	412	4	pistons	piston	NOUN
ap-9258	412	5	were	be	AUX
ap-9258	412	6	selected	select	VERB
ap-9258	412	7	while	while	SCONJ
ap-9258	412	8	the	the	DET
ap-9258	412	9	remaining	remain	VERB
ap-9258	412	10	two	two	NUM
ap-9258	412	11	were	be	AUX
ap-9258	412	12	left	leave	VERB
ap-9258	412	13	out	out	ADP
ap-9258	412	14	since	since	SCONJ
ap-9258	412	15	their	their	PRON
ap-9258	412	16	directional	directional	ADJ
ap-9258	412	17	factors	factor	NOUN
ap-9258	412	18	are	be	AUX
ap-9258	412	19	essentially	essentially	ADV
ap-9258	412	20	the	the	DET
ap-9258	412	21	same	same	ADJ
ap-9258	412	22	with	with	ADP
ap-9258	412	23	the	the	DET
ap-9258	412	24	polygons	polygon	NOUN
ap-9258	412	25	having	have	VERB
ap-9258	412	26	either	either	CCONJ
ap-9258	412	27	the	the	DET
ap-9258	412	28	odd	odd	ADJ
ap-9258	412	29	or	or	CCONJ
ap-9258	412	30	even	even	ADV
ap-9258	412	31	number	number	NOUN
ap-9258	412	32	of	of	ADP
ap-9258	412	33	sides	side	NOUN
ap-9258	412	34	and	and	CCONJ
ap-9258	412	35	their	their	PRON
ap-9258	412	36	performance	performance	NOUN
ap-9258	412	37	is	be	AUX
ap-9258	412	38	not	not	PART
ap-9258	412	39	dissimilar	dissimilar	ADJ
ap-9258	412	40	with	with	ADP
ap-9258	412	41	the	the	DET
ap-9258	412	42	heptagonal	heptagonal	ADJ
ap-9258	412	43	piston	piston	NOUN
ap-9258	412	44	.	.	PUNCT
ap-9258	413	1	each	each	PRON
ap-9258	413	2	of	of	ADP
ap-9258	413	3	the	the	DET
ap-9258	413	4	piston	piston	NOUN
ap-9258	413	5	surfaces	surface	NOUN
ap-9258	413	6	was	be	AUX
ap-9258	413	7	modelled	model	VERB
ap-9258	413	8	as	as	ADP
ap-9258	413	9	the	the	DET
ap-9258	413	10	head	head	NOUN
ap-9258	413	11	masses	masse	NOUN
ap-9258	413	12	of	of	ADP
ap-9258	413	13	a	a	DET
ap-9258	413	14	tonpilz	tonpilz	NOUN
ap-9258	413	15	transducer	transducer	NOUN
ap-9258	413	16	made	make	VERB
ap-9258	413	17	of	of	ADP
ap-9258	413	18	aluminium	aluminium	NOUN
ap-9258	413	19	using	use	VERB
ap-9258	413	20	the	the	DET
ap-9258	413	21	fem	fem	NOUN
ap-9258	413	22	as	as	SCONJ
ap-9258	413	23	shown	show	VERB
ap-9258	413	24	for	for	ADP
ap-9258	413	25	the	the	DET
ap-9258	413	26	standard	standard	ADJ
ap-9258	413	27	circular	circular	ADJ
ap-9258	413	28	source	source	NOUN
ap-9258	413	29	in	in	ADP
ap-9258	413	30	figure	figure	NOUN
ap-9258	413	31	14a	14a	NOUN
ap-9258	413	32	.	.	PUNCT
ap-9258	414	1	the	the	DET
ap-9258	414	2	tail	tail	NOUN
ap-9258	414	3	mass	mass	NOUN
ap-9258	414	4	at	at	ADP
ap-9258	414	5	the	the	DET
ap-9258	414	6	rear	rear	ADJ
ap-9258	414	7	end	end	NOUN
ap-9258	414	8	is	be	AUX
ap-9258	414	9	a	a	DET
ap-9258	414	10	brass	brass	NOUN
ap-9258	414	11	material	material	NOUN
ap-9258	414	12	serving	serve	VERB
ap-9258	414	13	as	as	ADP
ap-9258	414	14	a	a	DET
ap-9258	414	15	rigid	rigid	ADJ
ap-9258	414	16	baffle	baffle	NOUN
ap-9258	414	17	while	while	SCONJ
ap-9258	414	18	the	the	DET
ap-9258	414	19	piezo	piezo	PROPN
ap-9258	414	20	-	-	ADJ
ap-9258	414	21	ceramic	ceramic	ADJ
ap-9258	414	22	drive	drive	NOUN
ap-9258	414	23	section	section	NOUN
ap-9258	414	24	is	be	AUX
ap-9258	414	25	sandwiched	sandwich	VERB
ap-9258	414	26	inbetween	inbetween	ADJ
ap-9258	414	27	.	.	PUNCT
ap-9258	415	1	the	the	DET
ap-9258	415	2	selected	select	VERB
ap-9258	415	3	piezoelectric	piezoelectric	NOUN
ap-9258	415	4	ceramic	ceramic	ADJ
ap-9258	415	5	material	material	NOUN
ap-9258	415	6	was	be	AUX
ap-9258	415	7	kp14	kp14	PROPN
ap-9258	415	8	(	(	PUNCT
ap-9258	415	9	kyoungwon	kyoungwon	PROPN
ap-9258	415	10	ferrite	ferrite	PROPN
ap-9258	415	11	co.	co.	PROPN
ap-9258	415	12	ltd	ltd	PROPN
ap-9258	415	13	)	)	PUNCT
ap-9258	415	14	.	.	PUNCT
ap-9258	416	1	the	the	DET
ap-9258	416	2	head	head	NOUN
ap-9258	416	3	mass	mass	NOUN
ap-9258	416	4	was	be	AUX
ap-9258	416	5	designed	design	VERB
ap-9258	416	6	at	at	ADP
ap-9258	416	7	the	the	DET
ap-9258	416	8	equivalent	equivalent	ADJ
ap-9258	416	9	circular	circular	ADJ
ap-9258	416	10	diameter	diameter	NOUN
ap-9258	416	11	of	of	ADP
ap-9258	416	12	1.0λ	1.0λ	NUM
ap-9258	416	13	for	for	ADP
ap-9258	416	14	all	all	DET
ap-9258	416	15	the	the	DET
ap-9258	416	16	radiating	radiating	NOUN
ap-9258	416	17	surfaces	surface	NOUN
ap-9258	416	18	corresponding	correspond	VERB
ap-9258	416	19	to	to	ADP
ap-9258	416	20	the	the	DET
ap-9258	416	21	equivalent	equivalent	ADJ
ap-9258	416	22	surface	surface	NOUN
ap-9258	416	23	area	area	NOUN
ap-9258	416	24	derived	derive	VERB
ap-9258	416	25	for	for	ADP
ap-9258	416	26	each	each	DET
ap-9258	416	27	piston	piston	NOUN
ap-9258	416	28	source	source	NOUN
ap-9258	416	29	in	in	ADP
ap-9258	416	30	the	the	DET
ap-9258	416	31	theoretical	theoretical	ADJ
ap-9258	416	32	analysis	analysis	NOUN
ap-9258	416	33	.	.	PUNCT
ap-9258	417	1	since	since	SCONJ
ap-9258	417	2	the	the	DET
ap-9258	417	3	transducer	transducer	NOUN
ap-9258	417	4	vibrates	vibrate	VERB
ap-9258	417	5	in	in	ADP
ap-9258	417	6	the	the	DET
ap-9258	417	7	longitudinal	longitudinal	ADJ
ap-9258	417	8	mode	mode	NOUN
ap-9258	417	9	,	,	PUNCT
ap-9258	417	10	the	the	DET
ap-9258	417	11	thickness	thickness	NOUN
ap-9258	417	12	of	of	ADP
ap-9258	417	13	the	the	DET
ap-9258	417	14	drive	drive	NOUN
ap-9258	417	15	section	section	NOUN
ap-9258	417	16	and	and	CCONJ
ap-9258	417	17	all	all	DET
ap-9258	417	18	other	other	ADJ
ap-9258	417	19	dimensions	dimension	NOUN
ap-9258	417	20	were	be	AUX
ap-9258	417	21	determined	determine	VERB
ap-9258	417	22	by	by	ADP
ap-9258	417	23	the	the	DET
ap-9258	417	24	resonance	resonance	NOUN
ap-9258	417	25	frequency	frequency	NOUN
ap-9258	417	26	of	of	ADP
ap-9258	417	27	operation	operation	NOUN
ap-9258	417	28	.	.	PUNCT
ap-9258	418	1	for	for	ADP
ap-9258	418	2	the	the	DET
ap-9258	418	3	finite	finite	ADJ
ap-9258	418	4	element	element	NOUN
ap-9258	418	5	analysis	analysis	NOUN
ap-9258	418	6	(	(	PUNCT
ap-9258	418	7	fea	fea	NOUN
ap-9258	418	8	)	)	PUNCT
ap-9258	418	9	,	,	PUNCT
ap-9258	418	10	water	water	NOUN
ap-9258	418	11	was	be	AUX
ap-9258	418	12	modelled	model	VERB
ap-9258	418	13	at	at	ADP
ap-9258	418	14	the	the	DET
ap-9258	418	15	front	front	NOUN
ap-9258	418	16	of	of	ADP
ap-9258	418	17	each	each	DET
ap-9258	418	18	surface	surface	NOUN
ap-9258	418	19	as	as	SCONJ
ap-9258	418	20	shown	show	VERB
ap-9258	418	21	for	for	ADP
ap-9258	418	22	the	the	DET
ap-9258	418	23	standard	standard	ADJ
ap-9258	418	24	circular	circular	ADJ
ap-9258	418	25	head	head	NOUN
ap-9258	418	26	mass	mass	NOUN
ap-9258	418	27	in	in	ADP
ap-9258	418	28	figure	figure	NOUN
ap-9258	418	29	14b	14b	NUM
ap-9258	418	30	.	.	PUNCT
ap-9258	419	1	the	the	DET
ap-9258	419	2	final	final	ADJ
ap-9258	419	3	mesh	mesh	NOUN
ap-9258	419	4	of	of	ADP
ap-9258	419	5	the	the	DET
ap-9258	419	6	structure	structure	NOUN
ap-9258	419	7	was	be	AUX
ap-9258	419	8	simulated	simulate	VERB
ap-9258	419	9	at	at	ADP
ap-9258	419	10	an	an	DET
ap-9258	419	11	element	element	ADJ
ap-9258	419	12	size	size	NOUN
ap-9258	419	13	of	of	ADP
ap-9258	419	14	1	1	NUM
ap-9258	419	15	32	32	NUM
ap-9258	419	16	factor	factor	NOUN
ap-9258	419	17	of	of	ADP
ap-9258	419	18	the	the	DET
ap-9258	419	19	wavelength	wavelength	NOUN
ap-9258	419	20	.	.	PUNCT
ap-9258	420	1	the	the	DET
ap-9258	420	2	absorption	absorption	NOUN
ap-9258	420	3	boundary	boundary	ADJ
ap-9258	420	4	condition	condition	NOUN
ap-9258	420	5	was	be	AUX
ap-9258	420	6	applied	apply	VERB
ap-9258	420	7	all	all	ADV
ap-9258	420	8	around	around	ADP
ap-9258	420	9	the	the	DET
ap-9258	420	10	water	water	NOUN
ap-9258	420	11	to	to	PART
ap-9258	420	12	avoid	avoid	VERB
ap-9258	420	13	a	a	DET
ap-9258	420	14	loss	loss	NOUN
ap-9258	420	15	of	of	ADP
ap-9258	420	16	acoustic	acoustic	ADJ
ap-9258	420	17	signals	signal	NOUN
ap-9258	420	18	being	be	AUX
ap-9258	420	19	transmitted	transmit	VERB
ap-9258	420	20	through	through	ADP
ap-9258	420	21	the	the	DET
ap-9258	420	22	application	application	NOUN
ap-9258	420	23	of	of	ADP
ap-9258	420	24	a	a	DET
ap-9258	420	25	pressure	pressure	NOUN
ap-9258	420	26	pulse	pulse	NOUN
ap-9258	420	27	in	in	ADP
ap-9258	420	28	the	the	DET
ap-9258	420	29	form	form	NOUN
ap-9258	420	30	of	of	ADP
ap-9258	420	31	a	a	DET
ap-9258	420	32	sine	sine	ADJ
ap-9258	420	33	wave	wave	NOUN
ap-9258	420	34	function	function	NOUN
ap-9258	420	35	and	and	CCONJ
ap-9258	420	36	1	1	NUM
ap-9258	420	37	volt	volt	NOUN
ap-9258	420	38	of	of	ADP
ap-9258	420	39	electrical	electrical	ADJ
ap-9258	420	40	energy	energy	NOUN
ap-9258	420	41	to	to	PART
ap-9258	420	42	drive	drive	VERB
ap-9258	420	43	the	the	DET
ap-9258	420	44	ceramics	ceramic	NOUN
ap-9258	420	45	.	.	PUNCT
ap-9258	421	1	figure	figure	NOUN
ap-9258	421	2	15	15	NUM
ap-9258	421	3	shows	show	VERB
ap-9258	421	4	the	the	DET
ap-9258	421	5	models	model	NOUN
ap-9258	421	6	of	of	ADP
ap-9258	421	7	the	the	DET
ap-9258	421	8	selected	select	VERB
ap-9258	421	9	polygon	polygon	NOUN
ap-9258	421	10	surfaces	surface	NOUN
ap-9258	421	11	analysed	analyse	VERB
ap-9258	421	12	following	follow	VERB
ap-9258	421	13	similar	similar	ADJ
ap-9258	421	14	procedures	procedure	NOUN
ap-9258	421	15	.	.	PUNCT
ap-9258	422	1	the	the	DET
ap-9258	422	2	result	result	NOUN
ap-9258	422	3	of	of	ADP
ap-9258	422	4	the	the	DET
ap-9258	422	5	comparison	comparison	NOUN
ap-9258	422	6	between	between	ADP
ap-9258	422	7	the	the	DET
ap-9258	422	8	theoretical	theoretical	ADJ
ap-9258	422	9	beam	beam	NOUN
ap-9258	422	10	patterns	pattern	NOUN
ap-9258	422	11	and	and	CCONJ
ap-9258	422	12	that	that	PRON
ap-9258	422	13	obtained	obtain	VERB
ap-9258	422	14	from	from	ADP
ap-9258	422	15	the	the	DET
ap-9258	422	16	fea	fea	NOUN
ap-9258	422	17	for	for	ADP
ap-9258	422	18	each	each	PRON
ap-9258	422	19	of	of	ADP
ap-9258	422	20	the	the	DET
ap-9258	422	21	surfaces	surface	NOUN
ap-9258	422	22	are	be	AUX
ap-9258	422	23	shown	show	VERB
ap-9258	422	24	in	in	ADP
ap-9258	422	25	figure	figure	NOUN
ap-9258	422	26	16	16	NUM
ap-9258	422	27	.	.	PUNCT
ap-9258	422	28	except	except	SCONJ
ap-9258	422	29	with	with	ADP
ap-9258	422	30	a	a	DET
ap-9258	422	31	little	little	ADJ
ap-9258	422	32	difference	difference	NOUN
ap-9258	422	33	of	of	ADP
ap-9258	422	34	about	about	ADV
ap-9258	422	35	2	2	NUM
ap-9258	422	36	db	db	NOUN
ap-9258	422	37	in	in	ADP
ap-9258	422	38	the	the	DET
ap-9258	422	39	triangular	triangular	NOUN
ap-9258	422	40	case	case	NOUN
ap-9258	422	41	,	,	PUNCT
ap-9258	422	42	the	the	DET
ap-9258	422	43	excellent	excellent	ADJ
ap-9258	422	44	agreements	agreement	NOUN
ap-9258	422	45	observed	observe	VERB
ap-9258	422	46	in	in	ADP
ap-9258	422	47	figure	figure	NOUN
ap-9258	422	48	16	16	NUM
ap-9258	422	49	for	for	ADP
ap-9258	422	50	all	all	DET
ap-9258	422	51	the	the	DET
ap-9258	422	52	selected	select	VERB
ap-9258	422	53	cases	case	NOUN
ap-9258	422	54	is	be	AUX
ap-9258	422	55	a	a	DET
ap-9258	422	56	strong	strong	ADJ
ap-9258	422	57	attestation	attestation	NOUN
ap-9258	422	58	to	to	ADP
ap-9258	422	59	the	the	DET
ap-9258	422	60	validity	validity	NOUN
ap-9258	422	61	of	of	ADP
ap-9258	422	62	the	the	DET
ap-9258	422	63	directional	directional	ADJ
ap-9258	422	64	factors	factor	NOUN
ap-9258	422	65	invented	invent	VERB
ap-9258	422	66	for	for	ADP
ap-9258	422	67	the	the	DET
ap-9258	422	68	radiating	radiating	ADJ
ap-9258	422	69	polygonal	polygonal	ADJ
ap-9258	422	70	pistons	piston	NOUN
ap-9258	422	71	.	.	PUNCT
ap-9258	423	1	6	6	X
ap-9258	423	2	.	.	X
ap-9258	423	3	summary	summary	VERB
ap-9258	423	4	the	the	DET
ap-9258	423	5	directional	directional	ADJ
ap-9258	423	6	factors	factor	NOUN
ap-9258	423	7	of	of	ADP
ap-9258	423	8	acoustic	acoustic	ADJ
ap-9258	423	9	polygonal	polygonal	ADJ
ap-9258	423	10	piston	piston	NOUN
ap-9258	423	11	sources	source	NOUN
ap-9258	423	12	with	with	ADP
ap-9258	423	13	surfaces	surface	NOUN
ap-9258	423	14	ranging	range	VERB
ap-9258	423	15	from	from	ADP
ap-9258	423	16	three	three	NUM
ap-9258	423	17	to	to	PART
ap-9258	423	18	ten	ten	NUM
ap-9258	423	19	sides	side	NOUN
ap-9258	423	20	have	have	AUX
ap-9258	423	21	been	be	AUX
ap-9258	423	22	derived	derive	VERB
ap-9258	423	23	and	and	CCONJ
ap-9258	423	24	used	use	VERB
ap-9258	423	25	to	to	PART
ap-9258	423	26	characterise	characterise	VERB
ap-9258	423	27	their	their	PRON
ap-9258	423	28	radiation	radiation	NOUN
ap-9258	423	29	beam	beam	NOUN
ap-9258	423	30	patterns	pattern	NOUN
ap-9258	423	31	in	in	ADP
ap-9258	423	32	comparison	comparison	NOUN
ap-9258	423	33	with	with	ADP
ap-9258	423	34	the	the	DET
ap-9258	423	35	standard	standard	ADJ
ap-9258	423	36	circular	circular	ADJ
ap-9258	423	37	piston	piston	NOUN
ap-9258	423	38	.	.	PUNCT
ap-9258	424	1	with	with	ADP
ap-9258	424	2	the	the	DET
ap-9258	424	3	exception	exception	NOUN
ap-9258	424	4	of	of	ADP
ap-9258	424	5	the	the	DET
ap-9258	424	6	triangular	triangular	NOUN
ap-9258	424	7	surface	surface	NOUN
ap-9258	424	8	,	,	PUNCT
ap-9258	424	9	which	which	PRON
ap-9258	424	10	has	have	VERB
ap-9258	424	11	a	a	DET
ap-9258	424	12	unique	unique	ADJ
ap-9258	424	13	characteristics	characteristic	NOUN
ap-9258	424	14	,	,	PUNCT
ap-9258	424	15	the	the	DET
ap-9258	424	16	study	study	NOUN
ap-9258	424	17	indicates	indicate	VERB
ap-9258	424	18	that	that	SCONJ
ap-9258	424	19	(	(	PUNCT
ap-9258	424	20	a	a	NOUN
ap-9258	424	21	)	)	PUNCT
ap-9258	424	22	.	.	PUNCT
ap-9258	425	1	without	without	ADP
ap-9258	425	2	water	water	NOUN
ap-9258	425	3	.	.	PUNCT
ap-9258	426	1	(	(	PUNCT
ap-9258	426	2	b	b	NOUN
ap-9258	426	3	)	)	PUNCT
ap-9258	426	4	.	.	PUNCT
ap-9258	427	1	with	with	ADP
ap-9258	427	2	water	water	NOUN
ap-9258	427	3	.	.	PUNCT
ap-9258	428	1	figure	figure	VERB
ap-9258	428	2	14	14	NUM
ap-9258	428	3	.	.	PUNCT
ap-9258	429	1	finite	finite	PROPN
ap-9258	429	2	element	element	PROPN
ap-9258	429	3	model	model	NOUN
ap-9258	429	4	of	of	ADP
ap-9258	429	5	tonpilz	tonpilz	NOUN
ap-9258	429	6	with	with	ADP
ap-9258	429	7	a	a	DET
ap-9258	429	8	circular	circular	ADJ
ap-9258	429	9	head	head	NOUN
ap-9258	429	10	mass	mass	NOUN
ap-9258	429	11	diameter	diameter	NOUN
ap-9258	429	12	of	of	ADP
ap-9258	429	13	1.0λ	1.0λ	NUM
ap-9258	429	14	.	.	PUNCT
ap-9258	430	1	483	483	NUM
ap-9258	430	2	t.	t.	PROPN
ap-9258	430	3	a.	a.	PROPN
ap-9258	430	4	yusuf	yusuf	PROPN
ap-9258	430	5	,	,	PUNCT
ap-9258	430	6	s.	s.	PROPN
ap-9258	430	7	a.	a.	PROPN
ap-9258	430	8	aodu	aodu	PROPN
ap-9258	430	9	,	,	PUNCT
ap-9258	430	10	a.	a.	NOUN
ap-9258	430	11	o.	o.	PROPN
ap-9258	430	12	alabi	alabi	PROPN
ap-9258	430	13	acta	acta	PROPN
ap-9258	430	14	polytechnica	polytechnica	PROPN
ap-9258	430	15	(	(	PUNCT
ap-9258	430	16	a	a	NOUN
ap-9258	430	17	)	)	PUNCT
ap-9258	430	18	.	.	PUNCT
ap-9258	431	1	triangular	triangular	NOUN
ap-9258	431	2	.	.	PUNCT
ap-9258	432	1	(	(	PUNCT
ap-9258	432	2	b	b	NOUN
ap-9258	432	3	)	)	PUNCT
ap-9258	432	4	.	.	PUNCT
ap-9258	433	1	rectangular	rectangular	PROPN
ap-9258	433	2	.	.	PUNCT
ap-9258	434	1	(	(	PUNCT
ap-9258	434	2	c	c	NOUN
ap-9258	434	3	)	)	PUNCT
ap-9258	434	4	.	.	PUNCT
ap-9258	435	1	square	square	ADJ
ap-9258	435	2	.	.	PUNCT
ap-9258	436	1	(	(	PUNCT
ap-9258	436	2	d	d	NOUN
ap-9258	436	3	)	)	PUNCT
ap-9258	436	4	.	.	PUNCT
ap-9258	437	1	pentagonal	pentagonal	ADJ
ap-9258	437	2	.	.	PUNCT
ap-9258	438	1	(	(	PUNCT
ap-9258	438	2	e	e	NOUN
ap-9258	438	3	)	)	PUNCT
ap-9258	438	4	.	.	PUNCT
ap-9258	439	1	hexagonal	hexagonal	ADJ
ap-9258	439	2	.	.	PUNCT
ap-9258	440	1	(	(	PUNCT
ap-9258	440	2	f	f	X
ap-9258	440	3	)	)	PUNCT
ap-9258	440	4	.	.	PUNCT
ap-9258	441	1	heptagonal	heptagonal	ADJ
ap-9258	441	2	.	.	PUNCT
ap-9258	442	1	(	(	PUNCT
ap-9258	442	2	g	g	NOUN
ap-9258	442	3	)	)	PUNCT
ap-9258	442	4	.	.	PUNCT
ap-9258	443	1	octagonal	octagonal	ADJ
ap-9258	443	2	.	.	PUNCT
ap-9258	443	3	figure	figure	NOUN
ap-9258	443	4	15	15	NUM
ap-9258	443	5	.	.	PUNCT
ap-9258	444	1	the	the	DET
ap-9258	444	2	finite	finite	PROPN
ap-9258	444	3	element	element	NOUN
ap-9258	444	4	model	model	NOUN
ap-9258	444	5	of	of	ADP
ap-9258	444	6	tonpilz	tonpilz	NOUN
ap-9258	444	7	with	with	ADP
ap-9258	444	8	head	head	NOUN
ap-9258	444	9	mass	mass	NOUN
ap-9258	444	10	of	of	ADP
ap-9258	444	11	different	different	ADJ
ap-9258	444	12	radiating	radiate	VERB
ap-9258	444	13	polygon	polygon	NOUN
ap-9258	444	14	surfaces	surface	NOUN
ap-9258	444	15	of	of	ADP
ap-9258	444	16	equal	equal	ADJ
ap-9258	444	17	surface	surface	NOUN
ap-9258	444	18	areas	area	NOUN
ap-9258	444	19	with	with	ADP
ap-9258	444	20	the	the	DET
ap-9258	444	21	circular	circular	ADJ
ap-9258	444	22	head	head	NOUN
ap-9258	444	23	mass	mass	NOUN
ap-9258	444	24	diameter	diameter	NOUN
ap-9258	444	25	of	of	ADP
ap-9258	444	26	1.0λ	1.0λ	NUM
ap-9258	444	27	.	.	PUNCT
ap-9258	445	1	(	(	PUNCT
ap-9258	445	2	a	a	X
ap-9258	445	3	)	)	PUNCT
ap-9258	445	4	.	.	PUNCT
ap-9258	446	1	circular	circular	ADJ
ap-9258	446	2	.	.	PUNCT
ap-9258	447	1	(	(	PUNCT
ap-9258	447	2	b	b	NOUN
ap-9258	447	3	)	)	PUNCT
ap-9258	447	4	.	.	PUNCT
ap-9258	448	1	triangle	triangle	NOUN
ap-9258	448	2	.	.	PUNCT
ap-9258	449	1	(	(	PUNCT
ap-9258	449	2	c	c	NOUN
ap-9258	449	3	)	)	PUNCT
ap-9258	449	4	.	.	PUNCT
ap-9258	450	1	rectangular	rectangular	PROPN
ap-9258	450	2	.	.	PUNCT
ap-9258	451	1	(	(	PUNCT
ap-9258	451	2	d	d	NOUN
ap-9258	451	3	)	)	PUNCT
ap-9258	451	4	.	.	PUNCT
ap-9258	452	1	square	square	ADJ
ap-9258	452	2	.	.	PUNCT
ap-9258	453	1	(	(	PUNCT
ap-9258	453	2	e	e	NOUN
ap-9258	453	3	)	)	PUNCT
ap-9258	453	4	.	.	PUNCT
ap-9258	454	1	pentagonal	pentagonal	ADJ
ap-9258	454	2	.	.	PUNCT
ap-9258	455	1	(	(	PUNCT
ap-9258	455	2	f	f	X
ap-9258	455	3	)	)	PUNCT
ap-9258	455	4	.	.	PUNCT
ap-9258	456	1	hexagonal	hexagonal	ADJ
ap-9258	456	2	.	.	PUNCT
ap-9258	457	1	(	(	PUNCT
ap-9258	457	2	g	g	NOUN
ap-9258	457	3	)	)	PUNCT
ap-9258	457	4	.	.	PUNCT
ap-9258	458	1	heptagonal	heptagonal	ADJ
ap-9258	458	2	.	.	PUNCT
ap-9258	459	1	(	(	PUNCT
ap-9258	459	2	h	h	NOUN
ap-9258	459	3	)	)	PUNCT
ap-9258	459	4	.	.	PUNCT
ap-9258	460	1	octagonal	octagonal	ADJ
ap-9258	460	2	.	.	PUNCT
ap-9258	460	3	figure	figure	NOUN
ap-9258	460	4	16	16	NUM
ap-9258	460	5	.	.	PUNCT
ap-9258	461	1	the	the	DET
ap-9258	461	2	comparison	comparison	NOUN
ap-9258	461	3	between	between	ADP
ap-9258	461	4	the	the	DET
ap-9258	461	5	fea	fea	NOUN
ap-9258	461	6	and	and	CCONJ
ap-9258	461	7	theoretical	theoretical	ADJ
ap-9258	461	8	radiation	radiation	NOUN
ap-9258	461	9	beam	beam	NOUN
ap-9258	461	10	patterns	pattern	NOUN
ap-9258	461	11	of	of	ADP
ap-9258	461	12	different	different	ADJ
ap-9258	461	13	polygon	polygon	NOUN
ap-9258	461	14	surfaces	surface	NOUN
ap-9258	461	15	of	of	ADP
ap-9258	461	16	acoustic	acoustic	ADJ
ap-9258	461	17	piston	piston	NOUN
ap-9258	461	18	of	of	ADP
ap-9258	461	19	equal	equal	ADJ
ap-9258	461	20	surface	surface	NOUN
ap-9258	461	21	areas	area	NOUN
ap-9258	461	22	with	with	ADP
ap-9258	461	23	a	a	DET
ap-9258	461	24	circular	circular	ADJ
ap-9258	461	25	piston	piston	NOUN
ap-9258	461	26	diameter	diameter	NOUN
ap-9258	461	27	of	of	ADP
ap-9258	461	28	1.0λ	1.0λ	NUM
ap-9258	461	29	.	.	PUNCT
ap-9258	462	1	484	484	NUM
ap-9258	462	2	vol	vol	NOUN
ap-9258	462	3	.	.	PUNCT
ap-9258	463	1	64	64	NUM
ap-9258	463	2	no	no	NOUN
ap-9258	463	3	.	.	PUNCT
ap-9258	464	1	5/2024	5/2024	ADJ
ap-9258	464	2	acoustic	acoustic	ADJ
ap-9258	464	3	radiation	radiation	NOUN
ap-9258	464	4	beam	beam	NOUN
ap-9258	464	5	patterns	pattern	NOUN
ap-9258	464	6	of	of	ADP
ap-9258	464	7	different	different	ADJ
ap-9258	464	8	polygonal	polygonal	NOUN
ap-9258	464	9	.	.	PUNCT
ap-9258	464	10	.	.	PUNCT
ap-9258	464	11	.	.	PUNCT
ap-9258	465	1	even	even	ADV
ap-9258	465	2	-	-	PUNCT
ap-9258	465	3	sided	sided	ADJ
ap-9258	465	4	(	(	PUNCT
ap-9258	465	5	symmetrical	symmetrical	ADJ
ap-9258	465	6	)	)	PUNCT
ap-9258	465	7	and	and	CCONJ
ap-9258	465	8	odd	odd	ADV
ap-9258	465	9	-	-	PUNCT
ap-9258	465	10	sided	sided	ADJ
ap-9258	465	11	(	(	PUNCT
ap-9258	465	12	non	non	ADJ
ap-9258	465	13	-	-	ADJ
ap-9258	465	14	symmetrical	symmetrical	ADJ
ap-9258	465	15	)	)	PUNCT
ap-9258	465	16	polygons	polygon	NOUN
ap-9258	465	17	,	,	PUNCT
ap-9258	465	18	respectively	respectively	ADV
ap-9258	465	19	,	,	PUNCT
ap-9258	465	20	has	have	VERB
ap-9258	465	21	the	the	DET
ap-9258	465	22	general	general	ADJ
ap-9258	465	23	directional	directional	ADJ
ap-9258	465	24	factor	factor	NOUN
ap-9258	465	25	of	of	ADP
ap-9258	465	26	the	the	DET
ap-9258	465	27	form	form	NOUN
ap-9258	465	28	:	:	PUNCT
ap-9258	465	29	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ap-9258	465	30	sin	sin	NOUN
ap-9258	465	31	{	{	PUNCT
ap-9258	465	32	ka	ka	PROPN
ap-9258	465	33	tan	tan	PROPN
ap-9258	465	34	(	(	PUNCT
ap-9258	465	35	∅	∅	NOUN
ap-9258	465	36	2	2	X
ap-9258	465	37	)	)	PUNCT
ap-9258	465	38	sin	sin	NOUN
ap-9258	465	39	θ	θ	PROPN
ap-9258	465	40	}	}	PUNCT
ap-9258	465	41	ka	ka	PROPN
ap-9258	465	42	tan	tan	PROPN
ap-9258	465	43	(	(	PUNCT
ap-9258	465	44	∅	∅	NOUN
ap-9258	465	45	2	2	X
ap-9258	465	46	)	)	PUNCT
ap-9258	465	47	sin	sin	NOUN
ap-9258	465	48	θ	θ	PROPN
ap-9258	465	49	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ap-9258	465	50	,	,	PUNCT
ap-9258	465	51	and	and	CCONJ
ap-9258	465	52	:	:	PUNCT
ap-9258	465	53	sec	sec	PROPN
ap-9258	465	54	(	(	PUNCT
ap-9258	465	55	∅	∅	NOUN
ap-9258	465	56	2	2	X
ap-9258	465	57	)	)	PUNCT
ap-9258	465	58	1	1	NOUN
ap-9258	465	59	+	+	CCONJ
ap-9258	465	60			PROPN
ap-9258	465	61	sec	sec	PROPN
ap-9258	465	62	(	(	PUNCT
ap-9258	465	63	∅	∅	NOUN
ap-9258	465	64	2	2	NUM
ap-9258	465	65	)	)	PUNCT
ap-9258	466	1	−	−	PROPN
ap-9258	466	2	tan	tan	PROPN
ap-9258	466	3	(	(	PUNCT
ap-9258	466	4	∅	∅	NOUN
ap-9258	466	5	2	2	X
ap-9258	466	6	)	)	PUNCT
ap-9258	466	7	tan	tan	NOUN
ap-9258	466	8	∅	∅	NOUN
ap-9258	466	9			NOUN
ap-9258	466	10			NOUN
ap-9258	466	11	sin	sin	NOUN
ap-9258	466	12	{	{	PUNCT
ap-9258	466	13	ka	ka	PROPN
ap-9258	466	14	sec	sec	PROPN
ap-9258	466	15	(	(	PUNCT
ap-9258	466	16	∅	∅	NOUN
ap-9258	466	17	2	2	X
ap-9258	466	18	)	)	PUNCT
ap-9258	466	19	sin	sin	NOUN
ap-9258	466	20	θ	θ	PROPN
ap-9258	466	21	}	}	PUNCT
ap-9258	466	22	ka	ka	PROPN
ap-9258	466	23	sec	sec	PROPN
ap-9258	466	24	(	(	PUNCT
ap-9258	466	25	∅	∅	NOUN
ap-9258	466	26	2	2	X
ap-9258	466	27	)	)	PUNCT
ap-9258	466	28	sin	sin	NOUN
ap-9258	466	29	θ	θ	NOUN
ap-9258	466	30			NOUN
ap-9258	466	31	+	+	CCONJ
ap-9258	466	32	tan3	tan3	NOUN
ap-9258	466	33	(	(	PUNCT
ap-9258	466	34	∅	∅	NOUN
ap-9258	466	35	2	2	X
ap-9258	466	36	)	)	PUNCT
ap-9258	466	37			NOUN
ap-9258	466	38	sin	sin	NOUN
ap-9258	466	39	{	{	PUNCT
ap-9258	466	40	ka	ka	PROPN
ap-9258	466	41	tan	tan	PROPN
ap-9258	466	42	(	(	PUNCT
ap-9258	466	43	∅	∅	NOUN
ap-9258	466	44	2	2	X
ap-9258	466	45	)	)	PUNCT
ap-9258	466	46	sin	sin	NOUN
ap-9258	466	47	θ	θ	PROPN
ap-9258	466	48	}	}	PUNCT
ap-9258	466	49	ka	ka	PROPN
ap-9258	466	50	tan	tan	PROPN
ap-9258	466	51	(	(	PUNCT
ap-9258	466	52	∅	∅	NOUN
ap-9258	466	53	2	2	X
ap-9258	466	54	)	)	PUNCT
ap-9258	466	55	sin	sin	NOUN
ap-9258	466	56	θ	θ	NOUN
ap-9258	466	57			NOUN
ap-9258	466	58	−	−	PROPN
ap-9258	466	59	1	1	NUM
ap-9258	466	60	2	2	NUM
ap-9258	466	61	tan	tan	NOUN
ap-9258	466	62	∅	∅	NOUN
ap-9258	466	63			NOUN
ap-9258	466	64	sin	sin	NOUN
ap-9258	466	65	[	[	PUNCT
ap-9258	466	66	ka	ka	X
ap-9258	466	67	{	{	PUNCT
ap-9258	466	68	sec	sec	PROPN
ap-9258	466	69	(	(	PUNCT
ap-9258	466	70	∅	∅	NOUN
ap-9258	466	71	2	2	NUM
ap-9258	466	72	)	)	PUNCT
ap-9258	467	1	+	+	NOUN
ap-9258	467	2	tan	tan	PROPN
ap-9258	467	3	(	(	PUNCT
ap-9258	467	4	∅	∅	NOUN
ap-9258	467	5	2	2	NUM
ap-9258	467	6	)	)	PUNCT
ap-9258	467	7	2	2	NUM
ap-9258	467	8	}	}	PUNCT
ap-9258	467	9	sin	sin	NOUN
ap-9258	467	10	θ	θ	PROPN
ap-9258	467	11	]	]	PUNCT
ap-9258	468	1	ka	ka	PROPN
ap-9258	468	2	{	{	PUNCT
ap-9258	468	3	sec	sec	PROPN
ap-9258	468	4	(	(	PUNCT
ap-9258	468	5	∅	∅	NOUN
ap-9258	468	6	2	2	NUM
ap-9258	468	7	)	)	PUNCT
ap-9258	469	1	+	+	NOUN
ap-9258	469	2	tan	tan	PROPN
ap-9258	469	3	(	(	PUNCT
ap-9258	469	4	∅	∅	NOUN
ap-9258	469	5	2	2	NUM
ap-9258	469	6	)	)	PUNCT
ap-9258	469	7	2	2	NUM
ap-9258	469	8	}	}	PUNCT
ap-9258	469	9	sin	sin	NOUN
ap-9258	469	10	θ	θ	PROPN
ap-9258	469	11	·	·	PUNCT
ap-9258	469	12	sin	sin	X
ap-9258	469	13	[	[	PUNCT
ap-9258	469	14	ka	ka	X
ap-9258	469	15	{	{	PUNCT
ap-9258	469	16	sec	sec	PROPN
ap-9258	469	17	(	(	PUNCT
ap-9258	469	18	∅	∅	NOUN
ap-9258	469	19	2	2	NUM
ap-9258	469	20	)	)	PUNCT
ap-9258	469	21	−tan	−tan	PROPN
ap-9258	469	22	(	(	PUNCT
ap-9258	469	23	∅	∅	NOUN
ap-9258	469	24	2	2	NUM
ap-9258	469	25	)	)	PUNCT
ap-9258	469	26	2	2	NUM
ap-9258	469	27	}	}	PUNCT
ap-9258	469	28	sin	sin	NOUN
ap-9258	469	29	θ	θ	PROPN
ap-9258	469	30	]	]	PUNCT
ap-9258	470	1	ka	ka	PROPN
ap-9258	470	2	{	{	PUNCT
ap-9258	470	3	sec	sec	PROPN
ap-9258	470	4	(	(	PUNCT
ap-9258	470	5	∅	∅	NOUN
ap-9258	470	6	2	2	NUM
ap-9258	470	7	)	)	PUNCT
ap-9258	470	8	−tan	−tan	PROPN
ap-9258	470	9	(	(	PUNCT
ap-9258	470	10	∅	∅	NOUN
ap-9258	470	11	2	2	NUM
ap-9258	470	12	)	)	PUNCT
ap-9258	470	13	2	2	NUM
ap-9258	470	14	}	}	PUNCT
ap-9258	470	15	sin	sin	NOUN
ap-9258	470	16	θ	θ	PROPN
ap-9258	470	17			NOUN
ap-9258	470	18	,	,	PUNCT
ap-9258	470	19	where	where	SCONJ
ap-9258	470	20	a	a	PRON
ap-9258	470	21	is	be	AUX
ap-9258	470	22	the	the	DET
ap-9258	470	23	half	half	NOUN
ap-9258	470	24	of	of	ADP
ap-9258	470	25	the	the	DET
ap-9258	470	26	side	side	NOUN
ap-9258	470	27	length	length	NOUN
ap-9258	470	28	,	,	PUNCT
ap-9258	470	29	ϕ	ϕ	PROPN
ap-9258	470	30	is	be	AUX
ap-9258	470	31	the	the	DET
ap-9258	470	32	interior	interior	ADJ
ap-9258	470	33	angle	angle	NOUN
ap-9258	470	34	.	.	PUNCT
ap-9258	471	1	all	all	DET
ap-9258	471	2	the	the	DET
ap-9258	471	3	polygons	polygon	NOUN
ap-9258	471	4	show	show	VERB
ap-9258	471	5	a	a	DET
ap-9258	471	6	similar	similar	ADJ
ap-9258	471	7	performance	performance	NOUN
ap-9258	471	8	to	to	ADP
ap-9258	471	9	a	a	DET
ap-9258	471	10	circular	circular	ADJ
ap-9258	471	11	piston	piston	NOUN
ap-9258	471	12	of	of	ADP
ap-9258	471	13	a	a	DET
ap-9258	471	14	diameter	diameter	NOUN
ap-9258	471	15	not	not	PART
ap-9258	471	16	more	more	ADJ
ap-9258	471	17	than	than	ADP
ap-9258	471	18	0.28λ	0.28λ	NOUN
ap-9258	471	19	while	while	SCONJ
ap-9258	471	20	the	the	DET
ap-9258	471	21	same	same	ADJ
ap-9258	471	22	is	be	AUX
ap-9258	471	23	true	true	ADJ
ap-9258	471	24	for	for	ADP
ap-9258	471	25	all	all	PRON
ap-9258	471	26	but	but	SCONJ
ap-9258	471	27	the	the	DET
ap-9258	471	28	triangle	triangle	NOUN
ap-9258	471	29	when	when	SCONJ
ap-9258	471	30	the	the	DET
ap-9258	471	31	circular	circular	ADJ
ap-9258	471	32	diameter	diameter	NOUN
ap-9258	471	33	is	be	AUX
ap-9258	471	34	up	up	ADP
ap-9258	471	35	to	to	ADP
ap-9258	471	36	0.43λ	0.43λ	NOUN
ap-9258	471	37	.	.	PUNCT
ap-9258	472	1	in	in	ADP
ap-9258	472	2	terms	term	NOUN
ap-9258	472	3	of	of	ADP
ap-9258	472	4	the	the	DET
ap-9258	472	5	side	side	NOUN
ap-9258	472	6	lobe	lobe	PROPN
ap-9258	472	7	levels	level	NOUN
ap-9258	472	8	,	,	PUNCT
ap-9258	472	9	the	the	DET
ap-9258	472	10	radiating	radiate	VERB
ap-9258	472	11	beam	beam	NOUN
ap-9258	472	12	pattern	pattern	NOUN
ap-9258	472	13	of	of	ADP
ap-9258	472	14	the	the	DET
ap-9258	472	15	circular	circular	ADJ
ap-9258	472	16	piston	piston	NOUN
ap-9258	472	17	is	be	AUX
ap-9258	472	18	better	well	ADJ
ap-9258	472	19	than	than	ADP
ap-9258	472	20	all	all	DET
ap-9258	472	21	the	the	DET
ap-9258	472	22	polygons	polygon	NOUN
ap-9258	472	23	while	while	SCONJ
ap-9258	472	24	all	all	PRON
ap-9258	472	25	except	except	SCONJ
ap-9258	472	26	the	the	DET
ap-9258	472	27	triangle	triangle	NOUN
ap-9258	472	28	and	and	CCONJ
ap-9258	472	29	pentagon	pentagon	PROPN
ap-9258	472	30	are	be	AUX
ap-9258	472	31	identical	identical	ADJ
ap-9258	472	32	.	.	PUNCT
ap-9258	473	1	however	however	ADV
ap-9258	473	2	,	,	PUNCT
ap-9258	473	3	the	the	DET
ap-9258	473	4	beam	beam	NOUN
ap-9258	473	5	width	width	NOUN
ap-9258	473	6	of	of	ADP
ap-9258	473	7	the	the	DET
ap-9258	473	8	circular	circular	ADJ
ap-9258	473	9	piston	piston	NOUN
ap-9258	473	10	is	be	AUX
ap-9258	473	11	lower	low	ADJ
ap-9258	473	12	compared	compare	VERB
ap-9258	473	13	to	to	ADP
ap-9258	473	14	the	the	DET
ap-9258	473	15	rectangular	rectangular	ADJ
ap-9258	473	16	piston	piston	NOUN
ap-9258	473	17	and	and	CCONJ
ap-9258	473	18	almost	almost	ADV
ap-9258	473	19	identical	identical	ADJ
ap-9258	473	20	with	with	ADP
ap-9258	473	21	the	the	DET
ap-9258	473	22	square	square	ADJ
ap-9258	473	23	piston	piston	NOUN
ap-9258	473	24	when	when	SCONJ
ap-9258	473	25	the	the	DET
ap-9258	473	26	circular	circular	ADJ
ap-9258	473	27	diameter	diameter	NOUN
ap-9258	473	28	is	be	AUX
ap-9258	473	29	above	above	ADP
ap-9258	473	30	one	one	NUM
ap-9258	473	31	wavelength	wavelength	NOUN
ap-9258	473	32	.	.	PUNCT
ap-9258	474	1	the	the	DET
ap-9258	474	2	main	main	ADJ
ap-9258	474	3	beam	beam	NOUN
ap-9258	474	4	widths	width	NOUN
ap-9258	474	5	for	for	ADP
ap-9258	474	6	the	the	DET
ap-9258	474	7	non	non	ADJ
ap-9258	474	8	-	-	ADJ
ap-9258	474	9	symmetrical	symmetrical	ADJ
ap-9258	474	10	polygons	polygon	NOUN
ap-9258	474	11	are	be	AUX
ap-9258	474	12	relatively	relatively	ADV
ap-9258	474	13	narrower	narrow	ADJ
ap-9258	474	14	than	than	ADP
ap-9258	474	15	for	for	ADP
ap-9258	474	16	the	the	DET
ap-9258	474	17	symmetrical	symmetrical	ADJ
ap-9258	474	18	types	type	NOUN
ap-9258	474	19	.	.	PUNCT
ap-9258	475	1	7	7	X
ap-9258	475	2	.	.	X
ap-9258	475	3	conclusion	conclusion	NOUN
ap-9258	475	4	this	this	DET
ap-9258	475	5	study	study	NOUN
ap-9258	475	6	reveals	reveal	VERB
ap-9258	475	7	that	that	SCONJ
ap-9258	475	8	the	the	DET
ap-9258	475	9	perimeter	perimeter	NOUN
ap-9258	475	10	and	and	CCONJ
ap-9258	475	11	symmetry	symmetry	NOUN
ap-9258	475	12	of	of	ADP
ap-9258	475	13	the	the	DET
ap-9258	475	14	surface	surface	NOUN
ap-9258	475	15	are	be	AUX
ap-9258	475	16	the	the	DET
ap-9258	475	17	two	two	NUM
ap-9258	475	18	factors	factor	NOUN
ap-9258	475	19	that	that	PRON
ap-9258	475	20	combine	combine	VERB
ap-9258	475	21	to	to	PART
ap-9258	475	22	influence	influence	VERB
ap-9258	475	23	the	the	DET
ap-9258	475	24	radiating	radiate	VERB
ap-9258	475	25	beam	beam	NOUN
ap-9258	475	26	pattern	pattern	NOUN
ap-9258	475	27	of	of	ADP
ap-9258	475	28	an	an	DET
ap-9258	475	29	acoustic	acoustic	ADJ
ap-9258	475	30	piston	piston	NOUN
ap-9258	475	31	rather	rather	ADV
ap-9258	475	32	than	than	ADP
ap-9258	475	33	the	the	DET
ap-9258	475	34	surface	surface	NOUN
ap-9258	475	35	area	area	NOUN
ap-9258	475	36	or	or	CCONJ
ap-9258	475	37	the	the	DET
ap-9258	475	38	number	number	NOUN
ap-9258	475	39	of	of	ADP
ap-9258	475	40	sides	side	NOUN
ap-9258	475	41	.	.	PUNCT
ap-9258	476	1	hence	hence	ADV
ap-9258	476	2	,	,	PUNCT
ap-9258	476	3	the	the	DET
ap-9258	476	4	symmetrical	symmetrical	ADJ
ap-9258	476	5	polygonal	polygonal	ADJ
ap-9258	476	6	piston	piston	NOUN
ap-9258	476	7	surface	surface	NOUN
ap-9258	476	8	with	with	ADP
ap-9258	476	9	a	a	DET
ap-9258	476	10	higher	high	ADJ
ap-9258	476	11	perimeter	perimeter	NOUN
ap-9258	476	12	tends	tend	VERB
ap-9258	476	13	to	to	PART
ap-9258	476	14	have	have	VERB
ap-9258	476	15	a	a	DET
ap-9258	476	16	higher	high	ADJ
ap-9258	476	17	beamwidth	beamwidth	NOUN
ap-9258	476	18	and	and	CCONJ
ap-9258	476	19	is	be	AUX
ap-9258	476	20	,	,	PUNCT
ap-9258	476	21	therefore	therefore	ADV
ap-9258	476	22	,	,	PUNCT
ap-9258	476	23	most	most	ADV
ap-9258	476	24	recommended	recommend	VERB
ap-9258	476	25	in	in	ADP
ap-9258	476	26	the	the	DET
ap-9258	476	27	array	array	NOUN
ap-9258	476	28	designs	design	NOUN
ap-9258	476	29	for	for	ADP
ap-9258	476	30	applications	application	NOUN
ap-9258	476	31	where	where	SCONJ
ap-9258	476	32	larger	large	ADJ
ap-9258	476	33	area	area	NOUN
ap-9258	476	34	coverage	coverage	NOUN
ap-9258	476	35	is	be	AUX
ap-9258	476	36	desired	desire	VERB
ap-9258	476	37	.	.	PUNCT
ap-9258	477	1	the	the	DET
ap-9258	477	2	major	major	ADJ
ap-9258	477	3	implication	implication	NOUN
ap-9258	477	4	of	of	ADP
ap-9258	477	5	this	this	DET
ap-9258	477	6	study	study	NOUN
ap-9258	477	7	is	be	AUX
ap-9258	477	8	a	a	DET
ap-9258	477	9	more	more	ADV
ap-9258	477	10	efficient	efficient	ADJ
ap-9258	477	11	array	array	NOUN
ap-9258	477	12	transducer	transducer	NOUN
ap-9258	477	13	configuration	configuration	NOUN
ap-9258	477	14	using	use	VERB
ap-9258	477	15	the	the	DET
ap-9258	477	16	rectangle	rectangle	NOUN
ap-9258	477	17	,	,	PUNCT
ap-9258	477	18	triangle	triangle	NOUN
ap-9258	477	19	and	and	CCONJ
ap-9258	477	20	the	the	DET
ap-9258	477	21	rest	rest	NOUN
ap-9258	477	22	of	of	ADP
ap-9258	477	23	the	the	DET
ap-9258	477	24	polygons	polygon	NOUN
ap-9258	477	25	as	as	ADP
ap-9258	477	26	an	an	DET
ap-9258	477	27	alternative	alternative	NOUN
ap-9258	477	28	to	to	ADP
ap-9258	477	29	the	the	DET
ap-9258	477	30	circular	circular	ADJ
ap-9258	477	31	piston	piston	NOUN
ap-9258	477	32	of	of	ADP
ap-9258	477	33	equal	equal	ADJ
ap-9258	477	34	surface	surface	NOUN
ap-9258	477	35	area	area	NOUN
ap-9258	477	36	whose	whose	DET
ap-9258	477	37	diameter	diameter	NOUN
ap-9258	477	38	is	be	AUX
ap-9258	477	39	no	no	ADV
ap-9258	477	40	greater	great	ADJ
ap-9258	477	41	than	than	ADP
ap-9258	477	42	0.5λ	0.5λ	NOUN
ap-9258	477	43	,	,	PUNCT
ap-9258	477	44	0.28λ	0.28λ	NOUN
ap-9258	477	45	and	and	CCONJ
ap-9258	477	46	0.43λ	0.43λ	NOUN
ap-9258	477	47	respectively	respectively	ADV
ap-9258	477	48	.	.	PUNCT
ap-9258	478	1	this	this	DET
ap-9258	478	2	study	study	NOUN
ap-9258	478	3	does	do	AUX
ap-9258	478	4	not	not	PART
ap-9258	478	5	include	include	VERB
ap-9258	478	6	a	a	DET
ap-9258	478	7	parallelogram	parallelogram	NOUN
ap-9258	478	8	in	in	ADP
ap-9258	478	9	the	the	DET
ap-9258	478	10	analysis	analysis	NOUN
ap-9258	478	11	.	.	PUNCT
ap-9258	479	1	however	however	ADV
ap-9258	479	2	,	,	PUNCT
ap-9258	479	3	it	it	PRON
ap-9258	479	4	is	be	AUX
ap-9258	479	5	presumed	presume	VERB
ap-9258	479	6	that	that	SCONJ
ap-9258	479	7	it	it	PRON
ap-9258	479	8	would	would	AUX
ap-9258	479	9	have	have	VERB
ap-9258	479	10	the	the	DET
ap-9258	479	11	same	same	ADJ
ap-9258	479	12	directional	directional	ADJ
ap-9258	479	13	factor	factor	NOUN
ap-9258	479	14	and	and	CCONJ
ap-9258	479	15	exhibit	exhibit	VERB
ap-9258	479	16	the	the	DET
ap-9258	479	17	same	same	ADJ
ap-9258	479	18	beam	beam	NOUN
ap-9258	479	19	pattern	pattern	NOUN
ap-9258	479	20	as	as	ADP
ap-9258	479	21	the	the	DET
ap-9258	479	22	rectangle	rectangle	NOUN
ap-9258	479	23	due	due	ADP
ap-9258	479	24	to	to	ADP
ap-9258	479	25	their	their	PRON
ap-9258	479	26	nearly	nearly	ADV
ap-9258	479	27	similar	similar	ADJ
ap-9258	479	28	geometries	geometry	NOUN
ap-9258	479	29	.	.	PUNCT
ap-9258	480	1	references	reference	NOUN
ap-9258	480	2	[	[	X
ap-9258	480	3	1	1	NUM
ap-9258	480	4	]	]	PUNCT
ap-9258	480	5	b.-h	b.-h	NOUN
ap-9258	480	6	.	.	PUNCT
ap-9258	481	1	lee	lee	PROPN
ap-9258	481	2	,	,	PUNCT
ap-9258	481	3	j.-e	j.-e	PROPN
ap-9258	481	4	.	.	PUNCT
ap-9258	481	5	baek	baek	NOUN
ap-9258	481	6	,	,	PUNCT
ap-9258	481	7	d.-w	d.-w	PROPN
ap-9258	481	8	.	.	PUNCT
ap-9258	482	1	kim	kim	PROPN
ap-9258	482	2	,	,	PUNCT
ap-9258	482	3	et	et	PROPN
ap-9258	482	4	al	al	PROPN
ap-9258	482	5	.	.	PROPN
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ap-9258	482	7	design	design	NOUN
ap-9258	482	8	of	of	ADP
ap-9258	482	9	a	a	DET
ap-9258	482	10	sonar	sonar	ADJ
ap-9258	482	11	transmitter	transmitter	NOUN
ap-9258	482	12	for	for	ADP
ap-9258	482	13	the	the	DET
ap-9258	482	14	high	high	ADJ
ap-9258	482	15	-	-	PUNCT
ap-9258	482	16	power	power	NOUN
ap-9258	482	17	control	control	NOUN
ap-9258	482	18	of	of	ADP
ap-9258	482	19	multichannel	multichannel	ADJ
ap-9258	482	20	acoustic	acoustic	ADJ
ap-9258	482	21	transducers	transducer	NOUN
ap-9258	482	22	.	.	PUNCT
ap-9258	483	1	electronics	electronic	NOUN
ap-9258	483	2	10(21):2682	10(21):2682	ADP
ap-9258	483	3	,	,	PUNCT
ap-9258	483	4	2021	2021	NUM
ap-9258	483	5	.	.	PUNCT
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ap-9258	485	1	[	[	X
ap-9258	485	2	2	2	NUM
ap-9258	485	3	]	]	PUNCT
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ap-9258	485	5	p.	p.	NOUN
ap-9258	485	6	sarvazyan	sarvazyan	NOUN
ap-9258	485	7	,	,	PUNCT
ap-9258	485	8	m.	m.	NOUN
ap-9258	485	9	w.	w.	PROPN
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ap-9258	485	11	,	,	PUNCT
ap-9258	485	12	j.	j.	PROPN
ap-9258	485	13	f.	f.	PROPN
ap-9258	485	14	greenleaf	greenleaf	PROPN
ap-9258	485	15	.	.	PUNCT
ap-9258	486	1	acoustic	acoustic	ADJ
ap-9258	486	2	waves	wave	NOUN
ap-9258	486	3	in	in	ADP
ap-9258	486	4	medical	medical	ADJ
ap-9258	486	5	imaging	imaging	NOUN
ap-9258	486	6	and	and	CCONJ
ap-9258	486	7	diagnostics	diagnostic	NOUN
ap-9258	486	8	.	.	PUNCT
ap-9258	487	1	ultrasound	ultrasound	NOUN
ap-9258	487	2	in	in	ADP
ap-9258	487	3	medicine	medicine	NOUN
ap-9258	487	4	and	and	CCONJ
ap-9258	487	5	biology	biology	NOUN
ap-9258	487	6	39(7):1133–1146	39(7):1133–1146	NUM
ap-9258	487	7	,	,	PUNCT
ap-9258	487	8	2013	2013	NUM
ap-9258	487	9	.	.	PUNCT
ap-9258	488	1	https://doi.org/10.1016/j.ultrasmedbio.2013.02.006	https://doi.org/10.1016/j.ultrasmedbio.2013.02.006	PROPN
ap-9258	488	2	[	[	X
ap-9258	488	3	3	3	NUM
ap-9258	488	4	]	]	X
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ap-9258	488	6	kumar	kumar	PROPN
ap-9258	488	7	,	,	PUNCT
ap-9258	488	8	m.	m.	PROPN
ap-9258	488	9	azharudeen	azharudeen	PROPN
ap-9258	488	10	,	,	PUNCT
ap-9258	488	11	c.	c.	PROPN
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ap-9258	488	13	,	,	PUNCT
ap-9258	488	14	k.	k.	PROPN
ap-9258	488	15	subramani	subramani	PROPN
ap-9258	488	16	.	.	PUNCT
ap-9258	489	1	heat	heat	NOUN
ap-9258	489	2	transfer	transfer	NOUN
ap-9258	489	3	mechanism	mechanism	NOUN
ap-9258	489	4	driven	drive	VERB
ap-9258	489	5	by	by	ADP
ap-9258	489	6	acoustic	acoustic	ADJ
ap-9258	489	7	body	body	NOUN
ap-9258	489	8	force	force	NOUN
ap-9258	489	9	under	under	ADP
ap-9258	489	10	acoustic	acoustic	ADJ
ap-9258	489	11	fields	field	NOUN
ap-9258	489	12	.	.	PUNCT
ap-9258	490	1	physical	physical	ADJ
ap-9258	490	2	review	review	NOUN
ap-9258	490	3	fluids	fluid	NOUN
ap-9258	490	4	6:073501	6:073501	NUM
ap-9258	490	5	,	,	PUNCT
ap-9258	490	6	2021	2021	NUM
ap-9258	490	7	.	.	PUNCT
ap-9258	491	1	https://doi.org/10.1103/physrevfluids.6.073501	https://doi.org/10.1103/physrevfluids.6.073501	PROPN
ap-9258	491	2	[	[	PUNCT
ap-9258	491	3	4	4	NUM
ap-9258	491	4	]	]	PUNCT
ap-9258	491	5	x.	x.	NOUN
ap-9258	491	6	wang	wang	PROPN
ap-9258	491	7	,	,	PUNCT
ap-9258	491	8	j.	j.	PROPN
ap-9258	491	9	xu	xu	PROPN
ap-9258	491	10	,	,	PUNCT
ap-9258	491	11	j.	j.	PROPN
ap-9258	491	12	ding	ding	PROPN
ap-9258	491	13	,	,	PUNCT
ap-9258	491	14	et	et	PROPN
ap-9258	491	15	al	al	PROPN
ap-9258	491	16	.	.	PUNCT
ap-9258	492	1	a	a	DET
ap-9258	492	2	compact	compact	ADJ
ap-9258	492	3	and	and	CCONJ
ap-9258	492	4	low	low	ADJ
ap-9258	492	5	-	-	PUNCT
ap-9258	492	6	frequency	frequency	NOUN
ap-9258	492	7	acoustic	acoustic	ADJ
ap-9258	492	8	energy	energy	NOUN
ap-9258	492	9	harvester	harvester	NOUN
ap-9258	492	10	using	use	VERB
ap-9258	492	11	layered	layered	ADJ
ap-9258	492	12	acoustic	acoustic	ADJ
ap-9258	492	13	metamaterials	metamaterial	NOUN
ap-9258	492	14	.	.	PUNCT
ap-9258	493	1	smart	smart	ADJ
ap-9258	493	2	materials	material	NOUN
ap-9258	493	3	and	and	CCONJ
ap-9258	493	4	structures	structure	NOUN
ap-9258	493	5	28(2):025035	28(2):025035	NUM
ap-9258	493	6	,	,	PUNCT
ap-9258	493	7	2019	2019	NUM
ap-9258	493	8	.	.	PUNCT
ap-9258	493	9	https://doi.org/10.1088/1361-665x/aafbf6	https://doi.org/10.1088/1361-665x/aafbf6	X
ap-9258	494	1	[	[	X
ap-9258	494	2	5	5	NUM
ap-9258	494	3	]	]	PUNCT
ap-9258	494	4	a.	a.	NOUN
ap-9258	494	5	v.	v.	ADP
ap-9258	494	6	mikhaylov	mikhaylov	NOUN
ap-9258	494	7	,	,	PUNCT
ap-9258	494	8	y.	y.	PROPN
ap-9258	494	9	l.	l.	PROPN
ap-9258	494	10	gobov	gobov	PROPN
ap-9258	494	11	,	,	PUNCT
ap-9258	494	12	y.	y.	PROPN
ap-9258	494	13	g.	g.	PROPN
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ap-9258	494	17	s.	s.	PROPN
ap-9258	494	18	korzunin	korzunin	PROPN
ap-9258	494	19	.	.	PUNCT
ap-9258	495	1	electromagnetic	electromagnetic	ADJ
ap-9258	495	2	acoustic	acoustic	ADJ
ap-9258	495	3	transducers	transducer	NOUN
ap-9258	495	4	for	for	ADP
ap-9258	495	5	non	non	ADJ
ap-9258	495	6	-	-	ADJ
ap-9258	495	7	destructive	destructive	ADJ
ap-9258	495	8	testing	testing	NOUN
ap-9258	495	9	of	of	ADP
ap-9258	495	10	main	main	ADJ
ap-9258	495	11	pipelines	pipeline	NOUN
ap-9258	495	12	.	.	PUNCT
ap-9258	496	1	journal	journal	PROPN
ap-9258	496	2	of	of	ADP
ap-9258	496	3	physics	physics	PROPN
ap-9258	496	4	:	:	PUNCT
ap-9258	496	5	conference	conference	NOUN
ap-9258	496	6	series	series	PROPN
ap-9258	496	7	1636(1):012012	1636(1):012012	PROPN
ap-9258	496	8	,	,	PUNCT
ap-9258	496	9	2020	2020	NUM
ap-9258	496	10	.	.	PUNCT
ap-9258	497	1	https://doi.org/10.1088/1742-6596/1636/1/012012	https://doi.org/10.1088/1742-6596/1636/1/012012	X
ap-9258	498	1	[	[	X
ap-9258	498	2	6	6	NUM
ap-9258	498	3	]	]	PUNCT
ap-9258	498	4	a.	a.	NOUN
ap-9258	498	5	agi	agi	PROPN
ap-9258	498	6	,	,	PUNCT
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ap-9258	498	9	,	,	PUNCT
ap-9258	498	10	r.	r.	PROPN
ap-9258	498	11	shirazi	shirazi	PROPN
ap-9258	498	12	,	,	PUNCT
ap-9258	498	13	et	et	PROPN
ap-9258	498	14	al	al	PROPN
ap-9258	498	15	.	.	PROPN
ap-9258	498	16	comparative	comparative	ADJ
ap-9258	498	17	study	study	NOUN
ap-9258	498	18	of	of	ADP
ap-9258	498	19	ultrasound	ultrasound	PROPN
ap-9258	498	20	assisted	assist	VERB
ap-9258	498	21	water	water	NOUN
ap-9258	498	22	and	and	CCONJ
ap-9258	498	23	surfactant	surfactant	ADJ
ap-9258	498	24	flooding	flooding	NOUN
ap-9258	498	25	.	.	PUNCT
ap-9258	499	1	journal	journal	NOUN
ap-9258	499	2	of	of	ADP
ap-9258	499	3	king	king	PROPN
ap-9258	499	4	saud	saud	PROPN
ap-9258	499	5	university	university	PROPN
ap-9258	499	6	–	–	PUNCT
ap-9258	499	7	engineering	engineering	NOUN
ap-9258	499	8	sciences	science	NOUN
ap-9258	499	9	31(3):296–303	31(3):296–303	NUM
ap-9258	499	10	,	,	PUNCT
ap-9258	499	11	2019	2019	NUM
ap-9258	499	12	.	.	PUNCT
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ap-9258	500	2	[	[	X
ap-9258	500	3	7	7	NUM
ap-9258	500	4	]	]	X
ap-9258	500	5	y.	y.	PROPN
ap-9258	500	6	han	han	PROPN
ap-9258	500	7	,	,	PUNCT
ap-9258	500	8	x.	x.	PROPN
ap-9258	500	9	tian	tian	PROPN
ap-9258	500	10	,	,	PUNCT
ap-9258	500	11	f.	f.	PROPN
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ap-9258	500	13	,	,	PUNCT
ap-9258	500	14	et	et	PROPN
ap-9258	500	15	al	al	PROPN
ap-9258	500	16	.	.	PUNCT
ap-9258	501	1	a	a	DET
ap-9258	501	2	real	real	ADJ
ap-9258	501	3	-	-	PUNCT
ap-9258	501	4	time	time	NOUN
ap-9258	501	5	3	3	NUM
ap-9258	501	6	-	-	PUNCT
ap-9258	501	7	d	d	NOUN
ap-9258	501	8	underwater	underwater	ADJ
ap-9258	501	9	acoustical	acoustical	ADJ
ap-9258	501	10	imaging	imaging	NOUN
ap-9258	501	11	system	system	NOUN
ap-9258	501	12	.	.	PUNCT
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ap-9258	502	4	oceanic	oceanic	ADJ
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ap-9258	502	6	39(4):620–629	39(4):620–629	NUM
ap-9258	502	7	,	,	PUNCT
ap-9258	502	8	2014	2014	NUM
ap-9258	502	9	.	.	PUNCT
ap-9258	503	1	https://doi.org/10.1109/joe.2013.2285952	https://doi.org/10.1109/joe.2013.2285952	NOUN
ap-9258	503	2	485	485	NUM
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ap-9258	503	4	https://doi.org/10.1016/j.ultrasmedbio.2013.02.006	https://doi.org/10.1016/j.ultrasmedbio.2013.02.006	ADJ
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ap-9258	504	1	https://doi.org/10.1088/1742-6596/1636/1/012012	https://doi.org/10.1088/1742-6596/1636/1/012012	NUM
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ap-9258	504	4	t.	t.	PROPN
ap-9258	504	5	a.	a.	PROPN
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ap-9258	504	7	,	,	PUNCT
ap-9258	504	8	s.	s.	PROPN
ap-9258	504	9	a.	a.	PROPN
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ap-9258	505	1	[	[	X
ap-9258	505	2	8	8	NUM
ap-9258	505	3	]	]	X
ap-9258	505	4	h.	h.	PROPN
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ap-9258	505	8	h.	h.	PROPN
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ap-9258	505	10	,	,	PUNCT
ap-9258	505	11	w.	w.	PROPN
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ap-9258	505	19	application	application	NOUN
ap-9258	505	20	in	in	ADP
ap-9258	505	21	underwater	underwater	ADJ
ap-9258	505	22	acoustic	acoustic	ADJ
ap-9258	505	23	engineering	engineering	NOUN
ap-9258	505	24	.	.	PUNCT
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ap-9258	506	3	,	,	PUNCT
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ap-9258	506	5	.	.	PUNCT
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ap-9258	507	3	9	9	NUM
ap-9258	507	4	]	]	PUNCT
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ap-9258	507	7	-	-	PUNCT
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ap-9258	507	10	w.	w.	PROPN
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ap-9258	509	8	,	,	PUNCT
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ap-9258	511	2	10	10	NUM
ap-9258	511	3	]	]	X
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ap-9258	511	5	audoly	audoly	PROPN
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ap-9258	512	5	interactions	interaction	NOUN
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ap-9258	513	1	the	the	DET
ap-9258	513	2	journal	journal	NOUN
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ap-9258	513	10	,	,	PUNCT
ap-9258	513	11	1991	1991	NUM
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ap-9258	515	1	[	[	X
ap-9258	515	2	11	11	NUM
ap-9258	515	3	]	]	PUNCT
ap-9258	515	4	e.	e.	PROPN
ap-9258	515	5	e.	e.	PROPN
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ap-9258	515	7	,	,	PUNCT
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ap-9258	515	9	a.	a.	PROPN
ap-9258	515	10	b.	b.	PROPN
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ap-9258	515	13	j.	j.	PROPN
ap-9258	515	14	c.	c.	PROPN
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ap-9258	515	16	,	,	PUNCT
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ap-9258	515	18	buiochi	buiochi	PROPN
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ap-9258	516	1	acoustic	acoustic	ADJ
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ap-9258	516	4	of	of	ADP
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ap-9258	516	8	arrays	array	VERB
ap-9258	516	9	using	use	VERB
ap-9258	516	10	the	the	DET
ap-9258	516	11	impulse	impulse	ADJ
ap-9258	516	12	response	response	NOUN
ap-9258	516	13	and	and	CCONJ
ap-9258	516	14	the	the	DET
ap-9258	516	15	discrete	discrete	ADJ
ap-9258	516	16	representation	representation	NOUN
ap-9258	516	17	methods	method	NOUN
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ap-9258	517	1	journal	journal	NOUN
ap-9258	517	2	of	of	ADP
ap-9258	517	3	the	the	DET
ap-9258	517	4	brazilian	brazilian	ADJ
ap-9258	517	5	society	society	NOUN
ap-9258	517	6	of	of	ADP
ap-9258	517	7	mechanical	mechanical	ADJ
ap-9258	517	8	sciences	science	NOUN
ap-9258	517	9	and	and	CCONJ
ap-9258	517	10	engineering	engineer	VERB
ap-9258	517	11	33(4):408–416	33(4):408–416	NUM
ap-9258	517	12	,	,	PUNCT
ap-9258	517	13	2011	2011	NUM
ap-9258	517	14	.	.	PUNCT
ap-9258	518	1	https://doi.org/10.1590/s1678-58782011000400004	https://doi.org/10.1590/s1678-58782011000400004	PROPN
ap-9258	518	2	[	[	X
ap-9258	518	3	12	12	NUM
ap-9258	518	4	]	]	X
ap-9258	518	5	n.	n.	PROPN
ap-9258	518	6	t.	t.	PROPN
ap-9258	518	7	greene	greene	PROPN
ap-9258	518	8	,	,	PUNCT
ap-9258	518	9	g.	g.	PROPN
ap-9258	518	10	d.	d.	PROPN
ap-9258	518	11	paige	paige	PROPN
ap-9258	518	12	.	.	PUNCT
ap-9258	519	1	influence	influence	NOUN
ap-9258	519	2	of	of	ADP
ap-9258	519	3	sound	sound	ADJ
ap-9258	519	4	source	source	NOUN
ap-9258	519	5	width	width	NOUN
ap-9258	519	6	on	on	ADP
ap-9258	519	7	human	human	ADJ
ap-9258	519	8	sound	sound	NOUN
ap-9258	519	9	localization	localization	NOUN
ap-9258	519	10	.	.	PUNCT
ap-9258	520	1	in	in	ADP
ap-9258	520	2	2012	2012	NUM
ap-9258	520	3	annual	annual	ADJ
ap-9258	520	4	international	international	ADJ
ap-9258	520	5	conference	conference	NOUN
ap-9258	520	6	of	of	ADP
ap-9258	520	7	the	the	DET
ap-9258	520	8	ieee	ieee	NOUN
ap-9258	520	9	engineering	engineering	NOUN
ap-9258	520	10	in	in	ADP
ap-9258	520	11	medicine	medicine	NOUN
ap-9258	520	12	and	and	CCONJ
ap-9258	520	13	biology	biology	NOUN
ap-9258	520	14	society	society	NOUN
ap-9258	520	15	,	,	PUNCT
ap-9258	520	16	pp	pp	ADV
ap-9258	520	17	.	.	PUNCT
ap-9258	521	1	6455–6458	6455–6458	NUM
ap-9258	521	2	.	.	PUNCT
ap-9258	522	1	2012	2012	NUM
ap-9258	522	2	.	.	PUNCT
ap-9258	523	1	https://doi.org/10.1109/embc.2012.6347472	https://doi.org/10.1109/embc.2012.6347472	NOUN
ap-9258	524	1	[	[	X
ap-9258	524	2	13	13	NUM
ap-9258	524	3	]	]	X
ap-9258	524	4	i.	i.	PROPN
ap-9258	524	5	iliev	iliev	PROPN
ap-9258	524	6	.	.	PUNCT
ap-9258	525	1	polar	polar	ADJ
ap-9258	525	2	response	response	NOUN
ap-9258	525	3	of	of	ADP
ap-9258	525	4	a	a	DET
ap-9258	525	5	circular	circular	ADJ
ap-9258	525	6	piston	piston	NOUN
ap-9258	525	7	.	.	PUNCT
ap-9258	526	1	tem	tem	PROPN
ap-9258	526	2	journal	journal	PROPN
ap-9258	526	3	3(3):230–234	3(3):230–234	NUM
ap-9258	526	4	,	,	PUNCT
ap-9258	526	5	2014	2014	NUM
ap-9258	526	6	.	.	PUNCT
ap-9258	527	1	https://doi.org/10.18421/tem33-06	https://doi.org/10.18421/tem33-06	PRON
ap-9258	528	1	[	[	X
ap-9258	528	2	14	14	NUM
ap-9258	528	3	]	]	PUNCT
ap-9258	528	4	t.	t.	PROPN
ap-9258	528	5	douglas	douglas	PROPN
ap-9258	528	6	mast	mast	PROPN
ap-9258	528	7	,	,	PUNCT
ap-9258	528	8	f.	f.	PROPN
ap-9258	528	9	yu	yu	PROPN
ap-9258	528	10	.	.	PROPN
ap-9258	529	1	simplified	simplify	VERB
ap-9258	529	2	expansions	expansion	NOUN
ap-9258	529	3	for	for	ADP
ap-9258	529	4	radiation	radiation	NOUN
ap-9258	529	5	from	from	ADP
ap-9258	529	6	a	a	DET
ap-9258	529	7	baffled	baffled	ADJ
ap-9258	529	8	circular	circular	ADJ
ap-9258	529	9	piston	piston	NOUN
ap-9258	529	10	.	.	PUNCT
ap-9258	530	1	the	the	DET
ap-9258	530	2	journal	journal	NOUN
ap-9258	530	3	of	of	ADP
ap-9258	530	4	the	the	DET
ap-9258	530	5	acoustical	acoustical	ADJ
ap-9258	530	6	society	society	NOUN
ap-9258	530	7	of	of	ADP
ap-9258	530	8	america	america	PROPN
ap-9258	530	9	118(6):3457–3464	118(6):3457–3464	PROPN
ap-9258	530	10	,	,	PUNCT
ap-9258	530	11	2005	2005	NUM
ap-9258	530	12	.	.	PUNCT
ap-9258	531	1	https://doi.org/10.1121/1.2108997	https://doi.org/10.1121/1.2108997	PROPN
ap-9258	532	1	[	[	X
ap-9258	532	2	15	15	NUM
ap-9258	532	3	]	]	X
ap-9258	532	4	b.	b.	PROPN
ap-9258	532	5	nayak	nayak	PROPN
ap-9258	532	6	,	,	PUNCT
ap-9258	532	7	h.	h.	PROPN
ap-9258	532	8	gupta	gupta	PROPN
ap-9258	532	9	,	,	PUNCT
ap-9258	532	10	k.	k.	PROPN
ap-9258	532	11	roy	roy	PROPN
ap-9258	532	12	,	,	PUNCT
ap-9258	532	13	et	et	PROPN
ap-9258	532	14	al	al	PROPN
ap-9258	532	15	.	.	PUNCT
ap-9258	533	1	an	an	DET
ap-9258	533	2	experimental	experimental	ADJ
ap-9258	533	3	study	study	NOUN
ap-9258	533	4	of	of	ADP
ap-9258	533	5	the	the	DET
ap-9258	533	6	acoustic	acoustic	ADJ
ap-9258	533	7	field	field	NOUN
ap-9258	533	8	of	of	ADP
ap-9258	533	9	a	a	DET
ap-9258	533	10	single	single	ADJ
ap-9258	533	11	-	-	PUNCT
ap-9258	533	12	cell	cell	NOUN
ap-9258	533	13	piezoelectric	piezoelectric	NOUN
ap-9258	533	14	micromachined	micromachine	VERB
ap-9258	533	15	ultrasound	ultrasound	NOUN
ap-9258	533	16	transducer	transducer	NOUN
ap-9258	533	17	(	(	PUNCT
ap-9258	533	18	pmut	pmut	NOUN
ap-9258	533	19	)	)	PUNCT
ap-9258	533	20	.	.	PUNCT
ap-9258	534	1	in	in	ADP
ap-9258	534	2	2020	2020	NUM
ap-9258	534	3	5th	5th	ADJ
ap-9258	534	4	ieee	ieee	NOUN
ap-9258	534	5	international	international	ADJ
ap-9258	534	6	conference	conference	NOUN
ap-9258	534	7	on	on	ADP
ap-9258	534	8	emerging	emerge	VERB
ap-9258	534	9	electronics	electronic	NOUN
ap-9258	534	10	(	(	PUNCT
ap-9258	534	11	icee	icee	NOUN
ap-9258	534	12	)	)	PUNCT
ap-9258	534	13	,	,	PUNCT
ap-9258	534	14	pp	pp	PROPN
ap-9258	534	15	.	.	PUNCT
ap-9258	535	1	1–4	1–4	NUM
ap-9258	535	2	.	.	NOUN
ap-9258	535	3	2020	2020	NUM
ap-9258	535	4	.	.	PUNCT
ap-9258	536	1	https://doi.org/10.1109/icee50728.2020.9777041	https://doi.org/10.1109/icee50728.2020.9777041	PROPN
ap-9258	537	1	[	[	X
ap-9258	537	2	16	16	NUM
ap-9258	537	3	]	]	X
ap-9258	537	4	g.	g.	PROPN
ap-9258	537	5	zhao	zhao	PROPN
ap-9258	537	6	,	,	PUNCT
ap-9258	537	7	k.	k.	PROPN
ap-9258	537	8	shi	shi	PROPN
ap-9258	537	9	,	,	PUNCT
ap-9258	537	10	s.	s.	PROPN
ap-9258	537	11	zhong	zhong	PROPN
ap-9258	537	12	.	.	PUNCT
ap-9258	538	1	research	research	NOUN
ap-9258	538	2	on	on	ADP
ap-9258	538	3	array	array	NOUN
ap-9258	538	4	structures	structure	NOUN
ap-9258	538	5	of	of	ADP
ap-9258	538	6	acoustic	acoustic	ADJ
ap-9258	538	7	directional	directional	ADJ
ap-9258	538	8	transducer	transducer	NOUN
ap-9258	538	9	.	.	PUNCT
ap-9258	539	1	mathematical	mathematical	ADJ
ap-9258	539	2	problems	problem	NOUN
ap-9258	539	3	in	in	ADP
ap-9258	539	4	engineering	engineering	NOUN
ap-9258	539	5	2021(1):6670277	2021(1):6670277	NOUN
ap-9258	539	6	,	,	PUNCT
ap-9258	539	7	2021	2021	NUM
ap-9258	539	8	.	.	PUNCT
ap-9258	540	1	https://doi.org/10.1155/2021/6670277	https://doi.org/10.1155/2021/6670277	PROPN
ap-9258	541	1	[	[	X
ap-9258	541	2	17	17	NUM
ap-9258	541	3	]	]	X
ap-9258	541	4	r.	r.	PROPN
ap-9258	541	5	sharma	sharma	PROPN
ap-9258	541	6	,	,	PUNCT
ap-9258	541	7	r.	r.	PROPN
ap-9258	541	8	agarwal	agarwal	PROPN
ap-9258	541	9	,	,	PUNCT
ap-9258	541	10	a.	a.	PROPN
ap-9258	541	11	k.	k.	PROPN
ap-9258	541	12	dubey	dubey	PROPN
ap-9258	541	13	,	,	PUNCT
ap-9258	541	14	a.	a.	PROPN
ap-9258	541	15	arora	arora	PROPN
ap-9258	541	16	.	.	PUNCT
ap-9258	542	1	analytical	analytical	ADJ
ap-9258	542	2	modelling	modelling	NOUN
ap-9258	542	3	of	of	ADP
ap-9258	542	4	hexagonal	hexagonal	ADJ
ap-9258	542	5	shaped	shape	VERB
ap-9258	542	6	capacitive	capacitive	ADJ
ap-9258	542	7	micromachined	micromachine	VERB
ap-9258	542	8	ultrasonic	ultrasonic	ADJ
ap-9258	542	9	transducer	transducer	NOUN
ap-9258	542	10	.	.	PUNCT
ap-9258	543	1	international	international	ADJ
ap-9258	543	2	journal	journal	PROPN
ap-9258	543	3	of	of	ADP
ap-9258	543	4	system	system	NOUN
ap-9258	543	5	assurance	assurance	NOUN
ap-9258	543	6	engineering	engineering	NOUN
ap-9258	543	7	and	and	CCONJ
ap-9258	543	8	management	management	NOUN
ap-9258	543	9	12(2):252–262	12(2):252–262	NOUN
ap-9258	543	10	,	,	PUNCT
ap-9258	543	11	2021	2021	NUM
ap-9258	543	12	.	.	PUNCT
ap-9258	544	1	https://doi.org/10.1007/s13198-020-01046-y	https://doi.org/10.1007/s13198-020-01046-y	NOUN
ap-9258	545	1	[	[	X
ap-9258	545	2	18	18	NUM
ap-9258	545	3	]	]	X
ap-9258	545	4	r.	r.	PROPN
ap-9258	545	5	sharma	sharma	PROPN
ap-9258	545	6	,	,	PUNCT
ap-9258	545	7	r.	r.	PROPN
ap-9258	545	8	agarwal	agarwal	PROPN
ap-9258	545	9	,	,	PUNCT
ap-9258	545	10	a.	a.	PROPN
ap-9258	545	11	k.	k.	PROPN
ap-9258	545	12	dubey	dubey	PROPN
ap-9258	545	13	,	,	PUNCT
ap-9258	545	14	a.	a.	PROPN
ap-9258	545	15	arora	arora	PROPN
ap-9258	545	16	.	.	PUNCT
ap-9258	545	17	optimized	optimize	VERB
ap-9258	545	18	design	design	NOUN
ap-9258	545	19	of	of	ADP
ap-9258	545	20	cmut	cmut	NOUN
ap-9258	545	21	with	with	ADP
ap-9258	545	22	hexagonal	hexagonal	ADJ
ap-9258	545	23	membranes	membrane	NOUN
ap-9258	545	24	.	.	PUNCT
ap-9258	546	1	international	international	ADJ
ap-9258	546	2	journal	journal	NOUN
ap-9258	546	3	of	of	ADP
ap-9258	546	4	innovative	innovative	ADJ
ap-9258	546	5	technology	technology	NOUN
ap-9258	546	6	and	and	CCONJ
ap-9258	546	7	exploring	explore	VERB
ap-9258	546	8	engineering	engineering	NOUN
ap-9258	546	9	8(10):1805–1809	8(10):1805–1809	NUM
ap-9258	546	10	,	,	PUNCT
ap-9258	546	11	2019	2019	NUM
ap-9258	546	12	.	.	PUNCT
ap-9258	547	1	https://doi.org/10.35940/ijitee.j9194.0881019	https://doi.org/10.35940/ijitee.j9194.0881019	PROPN
ap-9258	547	2	[	[	X
ap-9258	547	3	19	19	NUM
ap-9258	547	4	]	]	X
ap-9258	547	5	y.	y.	PROPN
ap-9258	547	6	roh	roh	PROPN
ap-9258	547	7	,	,	PUNCT
ap-9258	547	8	m.	m.	PROPN
ap-9258	547	9	s.	s.	PROPN
ap-9258	547	10	afzal	afzal	PROPN
ap-9258	547	11	,	,	PUNCT
ap-9258	547	12	s.	s.	PROPN
ap-9258	547	13	r.	r.	PROPN
ap-9258	547	14	kwon	kwon	PROPN
ap-9258	547	15	.	.	PUNCT
ap-9258	548	1	analysis	analysis	NOUN
ap-9258	548	2	of	of	ADP
ap-9258	548	3	the	the	DET
ap-9258	548	4	effect	effect	NOUN
ap-9258	548	5	of	of	ADP
ap-9258	548	6	radiating	radiate	VERB
ap-9258	548	7	surface	surface	NOUN
ap-9258	548	8	geometry	geometry	NOUN
ap-9258	548	9	on	on	ADP
ap-9258	548	10	the	the	DET
ap-9258	548	11	beam	beam	NOUN
ap-9258	548	12	pattern	pattern	NOUN
ap-9258	548	13	of	of	ADP
ap-9258	548	14	underwater	underwater	ADJ
ap-9258	548	15	acoustic	acoustic	ADJ
ap-9258	548	16	transducers	transducer	NOUN
ap-9258	548	17	.	.	PUNCT
ap-9258	549	1	sensors	sensor	NOUN
ap-9258	549	2	and	and	CCONJ
ap-9258	549	3	actuators	actuator	NOUN
ap-9258	549	4	a	a	PRON
ap-9258	549	5	:	:	PUNCT
ap-9258	549	6	physical	physical	ADJ
ap-9258	549	7	330:112843	330:112843	NUM
ap-9258	549	8	,	,	PUNCT
ap-9258	549	9	2021	2021	NUM
ap-9258	549	10	.	.	PUNCT
ap-9258	550	1	https://doi.org/10.1016/j.sna.2021.112843	https://doi.org/10.1016/j.sna.2021.112843	PROPN
ap-9258	551	1	[	[	X
ap-9258	551	2	20	20	NUM
ap-9258	551	3	]	]	PUNCT
ap-9258	551	4	defence	defence	NOUN
ap-9258	551	5	research	research	NOUN
ap-9258	551	6	and	and	CCONJ
ap-9258	551	7	development	development	NOUN
ap-9258	551	8	organization	organization	NOUN
ap-9258	551	9	.	.	PUNCT
ap-9258	552	1	technologies	technology	NOUN
ap-9258	552	2	for	for	ADP
ap-9258	552	3	underwater	underwater	ADJ
ap-9258	552	4	surveillance	surveillance	NOUN
ap-9258	552	5	systems	system	NOUN
ap-9258	552	6	.	.	PUNCT
ap-9258	553	1	technology	technology	NOUN
ap-9258	553	2	focus	focus	VERB
ap-9258	553	3	25(2):1–28	25(2):1–28	NUM
ap-9258	553	4	,	,	PUNCT
ap-9258	553	5	2017	2017	NUM
ap-9258	553	6	.	.	PUNCT
ap-9258	554	1	[	[	X
ap-9258	554	2	21	21	NUM
ap-9258	554	3	]	]	X
ap-9258	554	4	r.	r.	PROPN
ap-9258	554	5	rajamäki	rajamäki	PROPN
ap-9258	554	6	,	,	PUNCT
ap-9258	554	7	v.	v.	PROPN
ap-9258	554	8	koivunen	koivunen	PROPN
ap-9258	554	9	.	.	PUNCT
ap-9258	555	1	sparse	sparse	VERB
ap-9258	555	2	active	active	ADJ
ap-9258	555	3	rectangular	rectangular	ADJ
ap-9258	555	4	array	array	NOUN
ap-9258	555	5	with	with	ADP
ap-9258	555	6	few	few	ADJ
ap-9258	555	7	closely	closely	ADV
ap-9258	555	8	spaced	space	VERB
ap-9258	555	9	elements	element	NOUN
ap-9258	555	10	.	.	PUNCT
ap-9258	556	1	ieee	ieee	NOUN
ap-9258	556	2	signal	signal	NOUN
ap-9258	556	3	processing	processing	NOUN
ap-9258	556	4	letters	letter	NOUN
ap-9258	556	5	25(12):1820–1824	25(12):1820–1824	NUM
ap-9258	556	6	,	,	PUNCT
ap-9258	556	7	2018	2018	NUM
ap-9258	556	8	.	.	PUNCT
ap-9258	557	1	https://doi.org/10.1109/lsp.2018.2876066	https://doi.org/10.1109/lsp.2018.2876066	VERB
ap-9258	558	1	[	[	X
ap-9258	558	2	22	22	NUM
ap-9258	558	3	]	]	PUNCT
ap-9258	558	4	m.-j	m.-j	PROPN
ap-9258	558	5	.	.	PUNCT
ap-9258	559	1	sim	sim	PROPN
ap-9258	559	2	,	,	PUNCT
ap-9258	559	3	c.	c.	PROPN
ap-9258	559	4	hong	hong	PROPN
ap-9258	559	5	,	,	PUNCT
ap-9258	559	6	w.-b	w.-b	PROPN
ap-9258	559	7	.	.	PUNCT
ap-9258	560	1	jeong	jeong	PROPN
ap-9258	560	2	.	.	PUNCT
ap-9258	560	3	hybrid	hybrid	ADJ
ap-9258	560	4	equivalent	equivalent	ADJ
ap-9258	560	5	circuit	circuit	NOUN
ap-9258	560	6	/	/	SYM
ap-9258	560	7	finite	finite	PROPN
ap-9258	560	8	element	element	NOUN
ap-9258	560	9	/	/	SYM
ap-9258	560	10	boundary	boundary	ADJ
ap-9258	560	11	element	element	NOUN
ap-9258	560	12	modeling	modeling	NOUN
ap-9258	560	13	for	for	ADP
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ap-9258	560	15	analysis	analysis	NOUN
ap-9258	560	16	of	of	ADP
ap-9258	560	17	an	an	DET
ap-9258	560	18	acoustic	acoustic	ADJ
ap-9258	560	19	transducer	transducer	NOUN
ap-9258	560	20	array	array	NOUN
ap-9258	560	21	with	with	ADP
ap-9258	560	22	flexible	flexible	ADJ
ap-9258	560	23	surrounding	surround	VERB
ap-9258	560	24	structures	structure	NOUN
ap-9258	560	25	.	.	PUNCT
ap-9258	561	1	applied	apply	VERB
ap-9258	561	2	sciences	science	NOUN
ap-9258	561	3	11(6):2702	11(6):2702	NUM
ap-9258	561	4	,	,	PUNCT
ap-9258	561	5	2021	2021	NUM
ap-9258	561	6	.	.	PUNCT
ap-9258	562	1	https://doi.org/10.3390/app11062702	https://doi.org/10.3390/app11062702	PROPN
ap-9258	563	1	[	[	X
ap-9258	563	2	23	23	NUM
ap-9258	563	3	]	]	PUNCT
ap-9258	563	4	t.	t.	PROPN
ap-9258	563	5	yokoyama	yokoyama	PROPN
ap-9258	563	6	,	,	PUNCT
ap-9258	563	7	m.	m.	NOUN
ap-9258	563	8	henmi	henmi	PROPN
ap-9258	563	9	,	,	PUNCT
ap-9258	563	10	a.	a.	PROPN
ap-9258	563	11	hasegawa	hasegawa	PROPN
ap-9258	563	12	,	,	PUNCT
ap-9258	563	13	t.	t.	PROPN
ap-9258	563	14	kikuchi	kikuchi	PROPN
ap-9258	563	15	.	.	PUNCT
ap-9258	564	1	effects	effect	NOUN
ap-9258	564	2	of	of	ADP
ap-9258	564	3	mutual	mutual	ADJ
ap-9258	564	4	interactions	interaction	NOUN
ap-9258	564	5	on	on	ADP
ap-9258	564	6	a	a	DET
ap-9258	564	7	phased	phase	VERB
ap-9258	564	8	transducer	transducer	NOUN
ap-9258	564	9	array	array	NOUN
ap-9258	564	10	.	.	PUNCT
ap-9258	565	1	japanese	japanese	ADJ
ap-9258	565	2	journal	journal	PROPN
ap-9258	565	3	of	of	ADP
ap-9258	565	4	applied	applied	ADJ
ap-9258	565	5	physics	physics	NOUN
ap-9258	565	6	37(5s):3166	37(5s):3166	NUM
ap-9258	565	7	,	,	PUNCT
ap-9258	565	8	1998	1998	NUM
ap-9258	565	9	.	.	PUNCT
ap-9258	566	1	https://doi.org/10.1143/jjap.37.3166	https://doi.org/10.1143/jjap.37.3166	NOUN
ap-9258	567	1	[	[	X
ap-9258	567	2	24	24	NUM
ap-9258	567	3	]	]	PUNCT
ap-9258	567	4	t.	t.	NOUN
ap-9258	567	5	beleyur	beleyur	NOUN
ap-9258	567	6	.	.	PUNCT
ap-9258	568	1	beamshapes	beamshape	NOUN
ap-9258	568	2	:	:	PUNCT
ap-9258	568	3	a	a	DET
ap-9258	568	4	python	python	NOUN
ap-9258	568	5	package	package	NOUN
ap-9258	568	6	to	to	PART
ap-9258	568	7	generate	generate	VERB
ap-9258	568	8	directivity	directivity	NOUN
ap-9258	568	9	patterns	pattern	NOUN
ap-9258	568	10	for	for	ADP
ap-9258	568	11	various	various	ADJ
ap-9258	568	12	sound	sound	ADJ
ap-9258	568	13	source	source	NOUN
ap-9258	568	14	models	model	NOUN
ap-9258	568	15	.	.	PUNCT
ap-9258	569	1	journal	journal	NOUN
ap-9258	569	2	of	of	ADP
ap-9258	569	3	open	open	ADJ
ap-9258	569	4	source	source	NOUN
ap-9258	569	5	software	software	NOUN
ap-9258	569	6	7(69):3740	7(69):3740	NOUN
ap-9258	569	7	,	,	PUNCT
ap-9258	569	8	2022	2022	NUM
ap-9258	569	9	.	.	PUNCT
ap-9258	569	10	https://doi.org/10.21105/joss.03740	https://doi.org/10.21105/joss.03740	NOUN
ap-9258	570	1	[	[	X
ap-9258	570	2	25	25	NUM
ap-9258	570	3	]	]	PUNCT
ap-9258	570	4	l.	l.	PROPN
ap-9258	570	5	e.	e.	PROPN
ap-9258	570	6	kinsler	kinsler	PROPN
ap-9258	570	7	,	,	PUNCT
ap-9258	570	8	a.	a.	PROPN
ap-9258	570	9	r.	r.	PROPN
ap-9258	570	10	frey	frey	PROPN
ap-9258	570	11	,	,	PUNCT
ap-9258	570	12	a.	a.	PROPN
ap-9258	570	13	b.	b.	PROPN
ap-9258	570	14	coppens	coppens	PROPN
ap-9258	570	15	,	,	PUNCT
ap-9258	570	16	j.	j.	PROPN
ap-9258	570	17	v.	v.	PROPN
ap-9258	570	18	sanders	sanders	PROPN
ap-9258	570	19	.	.	PUNCT
ap-9258	571	1	fundamentals	fundamental	NOUN
ap-9258	571	2	of	of	ADP
ap-9258	571	3	acoustics	acoustic	NOUN
ap-9258	571	4	.	.	PUNCT
ap-9258	572	1	john	john	PROPN
ap-9258	572	2	wiley	wiley	PROPN
ap-9258	572	3	&	&	CCONJ
ap-9258	572	4	sons	son	NOUN
ap-9258	572	5	,	,	PUNCT
ap-9258	572	6	new	new	PROPN
ap-9258	572	7	york	york	PROPN
ap-9258	572	8	,	,	PUNCT
ap-9258	572	9	usa	usa	PROPN
ap-9258	572	10	,	,	PUNCT
ap-9258	572	11	4th	4th	ADJ
ap-9258	572	12	edn	edn	NOUN
ap-9258	572	13	.	.	PUNCT
ap-9258	572	14	,	,	PUNCT
ap-9258	572	15	2000	2000	NUM
ap-9258	572	16	.	.	PUNCT
ap-9258	573	1	[	[	X
ap-9258	573	2	26	26	NUM
ap-9258	573	3	]	]	X
ap-9258	573	4	c.	c.	PROPN
ap-9258	573	5	deutsch	deutsch	PROPN
ap-9258	573	6	,	,	PUNCT
ap-9258	573	7	y.	y.	PROPN
ap-9258	573	8	gao	gao	PROPN
ap-9258	573	9	.	.	PUNCT
ap-9258	574	1	development	development	NOUN
ap-9258	574	2	of	of	ADP
ap-9258	574	3	a	a	DET
ap-9258	574	4	sonar	sonar	NOUN
ap-9258	574	5	for	for	ADP
ap-9258	574	6	underwater	underwater	ADJ
ap-9258	574	7	sensor	sensor	NOUN
ap-9258	574	8	platforms	platform	NOUN
ap-9258	574	9	and	and	CCONJ
ap-9258	574	10	surface	surface	NOUN
ap-9258	574	11	vehicles	vehicle	NOUN
ap-9258	574	12	.	.	PUNCT
ap-9258	575	1	master	master	NOUN
ap-9258	575	2	’s	’s	PART
ap-9258	575	3	thesis	thesis	NOUN
ap-9258	575	4	,	,	PUNCT
ap-9258	575	5	kth	kth	PROPN
ap-9258	575	6	royal	royal	PROPN
ap-9258	575	7	institute	institute	PROPN
ap-9258	575	8	of	of	ADP
ap-9258	575	9	technology	technology	PROPN
ap-9258	575	10	engineering	engineering	NOUN
ap-9258	575	11	sciences	science	NOUN
ap-9258	575	12	,	,	PUNCT
ap-9258	575	13	2017	2017	NUM
ap-9258	575	14	.	.	PUNCT
ap-9258	576	1	[	[	X
ap-9258	576	2	27	27	NUM
ap-9258	576	3	]	]	PUNCT
ap-9258	576	4	t.	t.	PROPN
ap-9258	576	5	mellow	mellow	PROPN
ap-9258	576	6	,	,	PUNCT
ap-9258	576	7	l.	l.	PROPN
ap-9258	576	8	kärkkäinen	kärkkäinen	PROPN
ap-9258	576	9	.	.	PUNCT
ap-9258	577	1	expansions	expansion	NOUN
ap-9258	577	2	for	for	ADP
ap-9258	577	3	the	the	DET
ap-9258	577	4	radiation	radiation	NOUN
ap-9258	577	5	impedance	impedance	NOUN
ap-9258	577	6	of	of	ADP
ap-9258	577	7	a	a	DET
ap-9258	577	8	rectangular	rectangular	ADJ
ap-9258	577	9	piston	piston	NOUN
ap-9258	577	10	in	in	ADP
ap-9258	577	11	an	an	DET
ap-9258	577	12	infinite	infinite	ADJ
ap-9258	577	13	baffle	baffle	NOUN
ap-9258	577	14	.	.	PUNCT
ap-9258	578	1	the	the	DET
ap-9258	578	2	journal	journal	NOUN
ap-9258	578	3	of	of	ADP
ap-9258	578	4	the	the	DET
ap-9258	578	5	acoustical	acoustical	ADJ
ap-9258	578	6	society	society	NOUN
ap-9258	578	7	of	of	ADP
ap-9258	578	8	america	america	PROPN
ap-9258	578	9	140(4):2867–2875	140(4):2867–2875	NUM
ap-9258	578	10	,	,	PUNCT
ap-9258	578	11	2016	2016	NUM
ap-9258	578	12	.	.	PUNCT
ap-9258	579	1	https://doi.org/10.1121/1.4964632	https://doi.org/10.1121/1.4964632	PROPN
ap-9258	580	1	[	[	X
ap-9258	580	2	28	28	NUM
ap-9258	580	3	]	]	X
ap-9258	580	4	n.	n.	PROPN
ap-9258	580	5	akkaya	akkaya	PROPN
ap-9258	580	6	.	.	PUNCT
ap-9258	581	1	acoustic	acoustic	ADJ
ap-9258	581	2	radiation	radiation	NOUN
ap-9258	581	3	from	from	ADP
ap-9258	581	4	baffled	baffled	ADJ
ap-9258	581	5	planar	planar	ADJ
ap-9258	581	6	sources	source	NOUN
ap-9258	581	7	:	:	PUNCT
ap-9258	581	8	a	a	DET
ap-9258	581	9	series	series	NOUN
ap-9258	581	10	approach	approach	NOUN
ap-9258	581	11	.	.	PUNCT
ap-9258	582	1	master	master	NOUN
ap-9258	582	2	’s	’s	PART
ap-9258	582	3	thesis	thesis	NOUN
ap-9258	582	4	,	,	PUNCT
ap-9258	582	5	texas	texas	PROPN
ap-9258	582	6	tech	tech	PROPN
ap-9258	582	7	university	university	PROPN
ap-9258	582	8	,	,	PUNCT
ap-9258	582	9	1999	1999	NUM
ap-9258	582	10	.	.	PUNCT
ap-9258	583	1	486	486	NUM
ap-9258	583	2	https://doi.org/10.3390/s20072148	https://doi.org/10.3390/s20072148	PROPN
ap-9258	583	3	https://doi.org/10.1088/1742-6596/1237/4/042063	https://doi.org/10.1088/1742-6596/1237/4/042063	PROPN
ap-9258	583	4	https://doi.org/10.1121/1.400543	https://doi.org/10.1121/1.400543	PROPN
ap-9258	583	5	https://doi.org/10.1590/s1678-58782011000400004	https://doi.org/10.1590/s1678-58782011000400004	PROPN
ap-9258	583	6	https://doi.org/10.1109/embc.2012.6347472	https://doi.org/10.1109/embc.2012.6347472	PROPN
ap-9258	583	7	https://doi.org/10.18421/tem33-06	https://doi.org/10.18421/tem33-06	ADP
ap-9258	583	8	https://doi.org/10.1121/1.2108997	https://doi.org/10.1121/1.2108997	PROPN
ap-9258	583	9	https://doi.org/10.1109/icee50728.2020.9777041	https://doi.org/10.1109/icee50728.2020.9777041	PROPN
ap-9258	583	10	https://doi.org/10.1155/2021/6670277	https://doi.org/10.1155/2021/6670277	PROPN
ap-9258	584	1	https://doi.org/10.1007/s13198-020-01046-y	https://doi.org/10.1007/s13198-020-01046-y	INTJ
ap-9258	584	2	https://doi.org/10.35940/ijitee.j9194.0881019	https://doi.org/10.35940/ijitee.j9194.0881019	ADV
ap-9258	584	3	https://doi.org/10.1016/j.sna.2021.112843	https://doi.org/10.1016/j.sna.2021.112843	PROPN
ap-9258	584	4	https://doi.org/10.1109/lsp.2018.2876066	https://doi.org/10.1109/lsp.2018.2876066	NOUN
ap-9258	584	5	https://doi.org/10.3390/app11062702	https://doi.org/10.3390/app11062702	NOUN
ap-9258	584	6	https://doi.org/10.1143/jjap.37.3166	https://doi.org/10.1143/jjap.37.3166	ADJ
ap-9258	584	7	https://doi.org/10.21105/joss.03740	https://doi.org/10.21105/joss.03740	NOUN
ap-9258	584	8	https://doi.org/10.1121/1.4964632	https://doi.org/10.1121/1.4964632	PROPN
ap-9258	584	9	acta	acta	PROPN
ap-9258	584	10	polytechnica	polytechnica	PROPN
ap-9258	584	11	64(5):470–486	64(5):470–486	NUM
ap-9258	584	12	,	,	PUNCT
ap-9258	584	13	2024	2024	NUM
ap-9258	584	14	1	1	NUM
ap-9258	584	15	introduction	introduction	NOUN
ap-9258	584	16	2	2	NUM
ap-9258	584	17	equivalent	equivalent	ADJ
ap-9258	584	18	surface	surface	NOUN
ap-9258	584	19	area	area	NOUN
ap-9258	584	20	of	of	ADP
ap-9258	584	21	the	the	DET
ap-9258	584	22	piston	piston	NOUN
ap-9258	584	23	sources	source	NOUN
ap-9258	584	24	3	3	NUM
ap-9258	584	25	derivation	derivation	NOUN
ap-9258	584	26	of	of	ADP
ap-9258	584	27	the	the	DET
ap-9258	584	28	directional	directional	ADJ
ap-9258	584	29	factors	factor	NOUN
ap-9258	584	30	of	of	ADP
ap-9258	584	31	the	the	DET
ap-9258	584	32	acoustic	acoustic	ADJ
ap-9258	584	33	piston	piston	NOUN
ap-9258	584	34	surfaces	surface	VERB
ap-9258	584	35	3.1	3.1	NUM
ap-9258	584	36	circular	circular	ADJ
ap-9258	584	37	piston	piston	NOUN
ap-9258	584	38	3.2	3.2	NUM
ap-9258	584	39	triangular	triangular	NOUN
ap-9258	584	40	piston	piston	NOUN
ap-9258	584	41	3.3	3.3	NUM
ap-9258	584	42	rectangular	rectangular	ADJ
ap-9258	584	43	and	and	CCONJ
ap-9258	584	44	square	square	ADJ
ap-9258	584	45	pistons	piston	NOUN
ap-9258	584	46	3.4	3.4	NUM
ap-9258	584	47	pentagonal	pentagonal	ADJ
ap-9258	584	48	piston	piston	NOUN
ap-9258	584	49	3.5	3.5	NUM
ap-9258	584	50	hexagonal	hexagonal	ADJ
ap-9258	584	51	piston	piston	NOUN
ap-9258	584	52	3.6	3.6	NUM
ap-9258	584	53	heptagonal	heptagonal	ADJ
ap-9258	584	54	piston	piston	NOUN
ap-9258	584	55	3.7	3.7	NUM
ap-9258	584	56	octagonal	octagonal	ADJ
ap-9258	584	57	piston	piston	NOUN
ap-9258	584	58	3.8	3.8	NUM
ap-9258	584	59	nonagonal	nonagonal	ADJ
ap-9258	584	60	piston	piston	NOUN
ap-9258	584	61	3.9	3.9	NUM
ap-9258	584	62	decagonal	decagonal	ADJ
ap-9258	584	63	piston	piston	NOUN
ap-9258	584	64	4	4	NUM
ap-9258	584	65	the	the	DET
ap-9258	584	66	analysis	analysis	NOUN
ap-9258	584	67	and	and	CCONJ
ap-9258	584	68	characterisation	characterisation	NOUN
ap-9258	584	69	of	of	ADP
ap-9258	584	70	the	the	DET
ap-9258	584	71	beam	beam	NOUN
ap-9258	584	72	patterns	pattern	NOUN
ap-9258	584	73	5	5	NUM
ap-9258	584	74	validation	validation	NOUN
ap-9258	584	75	by	by	ADP
ap-9258	584	76	finite	finite	PROPN
ap-9258	584	77	element	element	NOUN
ap-9258	584	78	method	method	NOUN
ap-9258	584	79	6	6	NUM
ap-9258	584	80	summary	summary	NOUN
ap-9258	584	81	7	7	NUM
ap-9258	584	82	conclusion	conclusion	NOUN
ap-9258	584	83	references	reference	NOUN