Spherical Waves
6.1 Introduction
Wave expansions in cylindrical and planar geometries consist of wavefronts which extend to infinity in at least one dimension. The spherical geometry provides a finite and compact expansion of wavefronts which allows us to gain an understanding of expanding waves. Furthermore, compact realistic vibrators are more closely modeled with spherical wave expansions than with planar or cylindrical expansions. We present in this chapter the solution of the wave equation in spherical coordinates, and detailed discussions of the radial functions, spherical harmonics and multipole expansions, the latter being very useful for low frequency modeling of radiation from compact vibrators.
The spherical wave spectrum, ...
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