Scattering of Acoustic Pulses by Rigid Spheres

Abstract

The scattered pressure field examined is that produced when a plane wave pulse is incident upon an ideally rigid sphere immersed in a fluid. The classical normal-mode series expresses the scattered field when a harmonic plane wave is incident upon the sphere. By using this series solution in conjunction with an incident pulse of known spectral content, it is possible, by numerical means, to synthesize exactly the resulting reflected pulse at an arbitrary field point. In the present instance, truncated sinusoidal incident pulses are considered, and scattered pulses are determined both at points close to the sphere and points distant from it. The time-varying amplitudes of these reflected pulses, thus rigorously calculated, are discussed in terms of a model based upon the existence of circumferential or “creeping” waves propagating along the periphery of the sphere. This model considers the reflected pulse to be composed from a specularly reflected replica of the incident pulse and attenuating pulses that travel along the periphery of the sphere from the boundary of the geometric shadow to the observation point.