Plane-wave diffraction by a rational wedge

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 π are given. The solution is expressed in terms of geometrical acoustic source terms and real integrals that represent the diffracted field. The expressions are in a form that allows easy calculation of the acoustic field. Uniformly valid expressions 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.