Acoustic scattering by inhomogeneous spheres

Abstract

Acoustic scattering problems are considered when the material parameters (density ρ and speed of sound c) are spherically symmetric functions of position. Explicit separated solutions are derived (i) when ρ(r)=exp(βr) and c−2 is a linear function of r−1, and (ii) when ρ(r)=exp(−βr2) 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.