Abstract
Acoustic scattering problems are considered when the material parameters (density rho and speed of sound c) are spherically symmetric functions of position. Explicit separated solutions are derived (i) when rho(r) = exp(beta r) and c(-2) is a linear function of r(-1), and (ii) when rho(r) = exp(-beta r2) and c(-2) is a linear function of r2. In both cases, the radial parts of the solutions are given in terms of Coulomb wave functions or Whittaker functions; these are well-studied special functions, closely related to confluent hypergeometric functions. Two problems are discussed in detail: scattering by an inhomogeneous sphere embedded in a homogeneous fluid, and scattering by a homogeneous sphere with a concentric inhomogeneous coating.
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