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

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2.13. Spherical coordinates

So far, we have only considered the one-dimensional spherical wave equation and its solution. In many problems where there are spherical surfaces but no axial or rotational symmetry, it is necessary to use spherical coordinates as shown in Fig. 2.19. The x, y, and z ordinates are replaced by spherical ordinates r, ϕ, and θ, where the radial ordinate r is given by
r = x 2 + y 2 + z 2 ,
image (2.174)
the inclination angle θ is given by
image
Figure 2.19 Spherical coordinates.
θ = arc cot ...

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