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

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12.4. Scattering from a rigid sphere by a point source

Refer to Fig. 12.6. Let a point source of volume velocity U ˜ 0 image be located at a distance d from a sphere of radius R. We wish to calculate the resultant pressure field p ˜ ( r , θ ) image at a distance r from the center of the sphere and at an angle θ with the axis passing through the point source and center of the sphere. The distance r 1 between the observation point and the point source is given by
Figure 12.6 Geometry of point source and sphere.

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