Scattering of a plane wave at a plane boundary presenting an impedance discontinuity

Abstract

The scattering of a sound wave by a boundary presenting an impedance discontinuity has been the object of many theoretical investigations based on the Wiener‐Hopf method. Although the method provides an exact solution, the expressions obtained are involved and not very useful in the vicinity of the boundary. The present work addresses the simple case of a plane wave incident on a plane boundary that is made up of two half‐planes. One of the half‐planes is perfectly rigid, the other is pressure release. The boundary between the two half‐planes is a straight line, and the medium over the boundary is a lossless fluid. It is shown that a simple analytical solution can be obtained by taking advantage of the symmetry properties of the problem. The solution is expressed in terms of one‐dimensional integrals that can be evaluated numerically. Numerical results for the sound pressure and velocity are presented. The case where the incident plane wave is replaced by a sound beam is briefly discussed. [Work supported...