Modern Fluid Dynamics for Physics and Astrophysics by Oded Regev Orkan M. Umurhan & Philip A. Yecko

Author:Oded Regev, Orkan M. Umurhan & Philip A. Yecko
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

(6.103)

because . The average total power radiated in this case is

(6.104)

where the closed surface over which the integration is taken has any form, so long as the source is inside it. Choosing the surface to be a sphere of radius r immediately gives the total sound power radiated by the point source in question:

(6.105)

2.Consider now the case in which the sound emitting body does not change its volume, e.g., it performs small oscillation to and fro in the fluid, a case which may include the complicated example of a flapping hummingbird wing. As explained above, the leading term is then the second (dipole) term, since a = 0. Thus we have the following expression coming from Eq. (6.99), valid near enough to the body:

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