Image-Based Solution for Scattering from a Wedge Satisfying Neumann Boundary Condition

Abstract

This work investigates the scattering of spherical waves from a two-dimensional wedge with an external angle greater than 180 degrees and less than 360 degrees. The expression for the Green's function in the frequency and time domain is obtained for a wedge with Neumann's boundary conditions. The image-based representation of reflections is incorporated to obtain a modified response which is valid and not limited to the incident angle, frequency, and observation location. It will be shown that the image-based expression for exact scattering is the simplest form, consists of six terms and an integral for diffraction. In this study, the exact decay in amplitude and propagation delay of the reflected wave is explained. It is shown that one does not need stationary phase approximation to obtain the response in the asymptotic limits.