Scattering of low-frequency spherical waves by fluid and solid spheres

Abstract

Acoustic Green’s functions for a homogeneous fluid with an embedded spherical obstacle arise in analyses of sound scattering by air bubbles, scattering by objects on or near the seafloor, radiation by finite sources, sound attenuation in and scattering from clouds of suspended particles, etc. Here, radius of the obstacle is assumed to be small compared to the wavelength of sound. This regime is usually referred to as Rayleigh scattering. A new, elementary solution of the problem of diffraction of a spherical wave was recently obtained for small, soft obstacles [O. A. Godin, J. Acoust. Soc. Am. 37, L13605 (2010)]. The solution is valid for arbitrary positions of the source and receiver relative to the obstacle. In this paper, the solution is extended to homogeneous and inhomogeneous fluid and solid spheres. Low-frequency scattering is found to be rather sensitive to boundary conditions on the surface of the obstacle. Resonance scattering of spherical waves by small spheres is investigated. [Work supported, in part, by ONR.]