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

TL;DR

This paper presents a new line integral formulation for the diffraction of waves by a right-angled impedance wedge, interpreting the solution as a superposition of edge sources, with modifications for surface wave effects.

Contribution

It transforms the Sommerfeld-Malyuzhinets integral into a physical edge source integral, extending the edge source concept to impedance wedges with surface wave considerations.

Findings

Exact solution expressed as a line integral over the wedge edge

Edge source interpretation extended to include surface wave contributions

Provides a physical insight into wave diffraction by impedance wedges

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 However, when surface waves are present the physical interpretation of the edge source integral must be altered: it no longer represents solely the diffracted field, but rather includes surface wave contributions.