An analytical decomposition of the Biot–Tolstoy edge diffraction model

Abstract

The sound field for a rigid, infinite wedge which is irradiated from a point source has an explicit impulse response solution which has been given by Biot and Tolstoy. This solution has been the basis for methods to calculate sound fields by summing up all specular reflections from finite surfaces and edge diffraction components from finite edge segments. However, these methods have usually relied on assumptions about the solution for finite edges. In this paper an edge diffraction model is presented which uses directional edge sources and analytical expressions for the directivities are derived to give exactly the Biot–Tolstoy solution for an infinite wedge. Unlike other models, with this new model explicit expressions can be found for certain geometries, such as the on-axis scattering from a rigid circular disc, for which both the first-order and the second-order edge diffraction can be derived. Furthermore, this model can be used to incorporate low-order edge diffraction into room acoustics prediction programs, which should improve them significantly at low frequencies.