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Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition
book

Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition

by Leo Beranek, Tim Mellow
May 2019
Intermediate to advanced content levelIntermediate to advanced
900 pages
29h 35m
English
Academic Press
Content preview from Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition

15.15. Radiation impedance

To derive the radiation impedance Z AR , we modify Eq. (13.212) from Section 13.10 for the uniform velocity distribution of a rigid piston to obtain that for one with a parabolic velocity distribution
Φ ( w ) = 2 ( 1 w 2 a 2 ) = 2 m = 0 ( δ m 0 δ m 1 ) ( w a ) 2 m , 0 w a
image (15.88)
and replace Eq. (13.215) with b(m   +   1)   =   2( δ m0   +   δ m1). By analyzing the low frequency asymptotic behavior, we obtain the radiation impedance elements
M A R = 8 ρ 0 5 π 2 a ,
(15.89)
C A R = 5 π a 3
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Publisher Resources

ISBN: 9780128152287