Plane wave diffraction by a rational wedge

Abstract

In this paper new expressions for the acoustic field produced when a plane wave source of sound is diffracted by a soft, hard or mixed soft/hard wedge whose angle can be expressed as a rational multiple of are given. The solution is expressed in terms of geometrical acoustic source terms and real integrals which represent the diffracted field. The expressions are in a form which allows easy calculation of the acoustic field. Uniformly valid ex-pressions for the far field are also given for all values of the angular variable. The general result obtained includes as special cases, Sommerfeld' s solution for diffraction by a half plane, Reiche’s result for the diffraction by a right angled wedge, and a new representation for the solution of the problem of diffraction by a mixed soft/hard half plane.