id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ap-368	Koníček, P.; Bednařík, M.; Červenka, M.	Propagation of Quasi-plane Nonlinear Waves in Tubes	2002	9	.pdf	application/pdf	6242	307	66	The solution of the linearized GBE for the boundary con- dition � � � �v vz zm0, sin� ��� can be expressed as � �� � � �v v z zz zm� � � �exp sin� � �� �b b . (32) where � is the attenuation coefficient for the classical thermo- -viscous loss mechanism � � � � b c 2 0 0 32 (33) and the attenuation coefficient �b represents the losses due to the wall friction � �b � �B . The cut-off frequency of the first symmetric mode in a cir- cular waveguide is given by the formula f c k c Rm1 � � �0 1 0 02 2� � � � , (36) where k1 is the radial wave number of the first mode and � ��� � .38317 is the first zero point of the Bessel function derivative: � �� � �J0 0�� .	cache/ap-368.pdf	txt/ap-368.txt