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Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition by Tim Mellow, Leo Beranek

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Part XXXIV: Radiation and scattering in spherical coordinates

12.3. Scattering of a plane wave from a rigid sphere

In this example, the expression scattering has been applied rather than reflection because not only does a sphere reflect sound but sound waves can bend around it, a phenomenon known as diffraction. Generally, scattering refers to a mixture of reflection and diffraction. In the case of reflection from a plane (see Section 4.9), we used rectangular coordinates in x and y. Here, we are considering a sphere [1], so it is convenient to use axially symmetrical spherical coordinates in r and θ as shown in Fig. 12.1. In general, the solution for the resultant field is the sum of the incident field in the absence of any obstacle and ...

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