Scattering of a Plane Acoustical Wave by a Spherical Obstacle

The long-time behavior of the scattered field produced by a plane acoustical pulse stalking a spherical obstacle is investigated. Incident pulses are taken that represent a unit step in potential (or equivalently delta function pulse in pressure), an arbitrary potential pulse of finite duration, and an arbitrary pressure pulse of finite duration. Both hard and soft spheres are considered. In addition, a pulse consisting of a unit step in velocity impinging on a hard sphere is examined. In each case, the time rate of decay to the steady state is established. This is seen to be controlled by the zeroes of certain naturally occurring special polynomials that arise because of the spherical geometry and are independent of the shape of the incident pulse