Interaction of an inhomogeneous acoustic plane wave with a fluid sphere: Analytical solution

Abstract

The problem of scattering of a plane acoustic wave by a fluid sphere was addressed by V. C. Anderson [J. Acoust. Soc. Am. 22, 426 (1950)]. This wave was assumed to be homogeneous, without amplitude variation over the wave front. The problem of scattering of a plane wave partially insonifying a rigid sphere was addressed by G. C. Gaunaurd [IEEE J. Oceanic Eng. 10, 213 (1985)], but in the Kirchhoff approximation. Here, the problem of scattering of an inhomogeneous plane acoustic wave by a fluid sphere is addressed. A general analytical solution is given. A particular solution is described for a monochromatic plane wave whose amplitude on the surface of a sphere of radius r=a, with center at the origin, is exp[ika cos θ−2αa cos2(θ/2)], where k is the wavenumber, θ is measured relative to the direction of propagation, and α is the absorption coefficient. Both the scattered and internal fields are evaluated for a range of parameter values of k, α, r, and θ, and compared against the Anderson solution for a homogeneous plane wave. It is believed that H. Medwin would have appreciated the unexpressed direction of this work: modeling of sonar interactions with marine animals.