Integral identities for reflection, transmission and scattering coefficients

TL;DR

This paper derives integral identities for acoustic scattering, linking frequency-integrated physical quantities like transmission loss to spatial averages, unifying known identities under a general framework.

Contribution

It introduces a general method to derive integral identities for acoustic scattering, encompassing known results as special cases.

Findings

Integral of transmission loss expressed via spatial averages.

Known identities for extinction cross section derived as special cases.

Unified framework for integral identities in acoustic scattering.

Abstract

Several integral identities related to acoustic scattering are presented. In each case the identity involves the integral over frequency of a physical quantity. For instance, the integrated transmission loss, a measure of the transmitted acoustic energy through an inhomogeneous layer, is shown to have a simple expression in terms of spatially averaged physical quantities. Known identities for the extinction cross section and for the acoustic energy loss in a slab with a rigid backing, are shown to be special cases of a general procedure for finding such integral identities.