Singularities in first-order wedge-diffraction expressions within narrow, finite 3D wedges

摘要

The field resulting from propagating sound interacting with a wedge is often decomposed into geometrical-acoustics (GA) and diffracted components. With such a decomposition, singularities in mathematical expressions for the latter typically are explained as necessary to compensate for discontinuities in the GA field at the two shadow boundaries and the two first-order reflection boundaries corresponding to the two wedge faces. However, these singularities result from periodic functions and thus can be associated with additional, higher-order GA components. In this short communication we describe the relationship between the periodicity of the diffraction singularities and higher-order reflections, which is relevant to the analysis of wedges with open angle less than π. The discussion is provided specifically in the context of finite, three-dimensional wedges.