Diffraction by a right-angled impedance wedge: an edge source formulation

Abstract

This paper concerns the frequency domain problem of diffraction of a plane wave incident on an infinite right-angled wedge on which impedance (absorbing) boundary conditions are imposed. It is demonstrated that the exact Sommerfeld-Malyuzhinets contour integral solution for the diffracted field can be transformed to a line integral over a physical variable along the diffracting edge. This integral can be interpreted as a superposition of secondary point sources (with directivity) positioned along the edge, in the spirit of the edge source formulations for rigid (sound-hard) wedges derived in [Svensson et al., Acta Acustica/Acustica 95, 2009, pp.~568-572]. However, when surface waves are present the physical interpretation of the edge source integral must be altered: it no longer represents solely the diffracted field, but rather includes surface wave contributions.