Spherical wave diffraction by a rational wedge

Abstract

In this paper we derive a new expression for the point source Green's function for the reduced wave equation, valid in an angular sector, whoseangle is equal to a rational multiple of . This Green's function is used to find new expressions for the field produced by the diffraction of a spherical wave source by a wedge, whose angle can be expressed as a rational multiple of . The expressions obtained are in the form of source terms and real integrals which represent the diffracted field. The general resultobtained includes as special cases Macdonald’s solution for diffraction by ahalf plane; a solution for the problem of diffraction by a wedge of open angle 3/2, i.e. a corner; a new representation for the solution of the problemof diffraction by a mixed soft/hard half plane; and a new representation for the point source Green's function for Laplace's equation, valid in an angularsector whose angle is equal to a rational multiple of .