Acoustic scattering theory without large-distance asymptotics

TL;DR

This paper develops a rigorous acoustic scattering theory that does not rely on large-distance asymptotics, preserving distance information and improving the description of wave behavior near targets.

Contribution

It introduces a new theoretical framework for acoustic scattering that accounts for near-target effects, unlike traditional methods that use asymptotic approximations.

Findings

Near target effects significantly influence angular wave distribution.

The theory improves accuracy for long wavelength acoustic scattering.

Examples include scattering on rigid and nonrigid spheres.

Abstract

In conventional acoustic scattering theory, a large-distance asymptotic approximation is employed. In this approximation, a far-field pattern, an asymptotic approximation of the exact result, is used to describe a scattering process. The information of the distance between the target and the observer, however, is lost in the large-distance asymptotic approximation. In this paper, we provide a rigorous theory of acoustic scattering without the large-distance asymptotic approximation. The acoustic scattering treatment developed in this paper provides an improved description for the acoustic wave outside the target. Moreover, as examples, we consider acoustic scattering on a rigid sphere and on a nonrigid sphere. We also illustrate the influence of the near target effect on the angular distribution of outgoing waves. It is shown that for long wavelength acoustic scattering, the near target effect must be reckoned in.