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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

14.6. Membrane wave equation in polar coordinates

As the Laplace operator of Eq. (14.5) is the same as that of the wave equation in three dimensions given by Eq. (2.147) but without the z-term, it follows that the Laplace operator for the membrane in polar coordinates, which is given by
2 = 2 w 2 + 1 w w + 1 w 2 2 ϕ 2 .
image (14.25)
A rigorous derivation of this is given in Ref. [1]. Following the same procedure as in Section 2.10, where we separate the wave equation into its radial and angular (azimuthal) parts, we arrive at the solution to the homogeneous membrane wave equation
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Publisher Resources

ISBN: 9780128152287