Acoustic scattering at a gap between two orthogonal, semi-infinite barriers: coordinate and spectral equations

Abstract

The 2-D problem of diffraction by a gap between two orthogonal semi-infinite barriers is considered. The method of reflections is applied and the diffraction problem is reformulated as a propagation problem on a multi-sheet surface. An auxiliary problem, with a single incident wave, is formulated. By applying an embedding formula the auxiliary problem is reduced to that of finding a set of edge Green’s functions for the surface. The edge Green’s functions are proven to satisfy two sets of differential equations: the coordinate equations and the spectral equation. Although too complicated to be solved analytically, these ordinary differential equations offer some advantages over partial differential equations or integral equations.