Image Based Theory of Scattering from Planar Surfaces with Application to Room Impulse Responses

In this dissertation analytical and numerical models of the acoustic impulse response for geometries comprised of mutually perpendicular planar boundaries is presented. The solution process utilizes the method of images in conjunction with the inverse Laplace transform of the reflection coefficient. It is shown that the amplitude of each image source can be evaluated through complex integration of the reflection coefficient along branch lines in the wavenumber plane. The integration path is a function of the speed of sound of the reflecting plane. A new representation of the Green's function for multiple reflections of spherical waves from planar surfaces is derived. This is applied to derive a rigorous solution for the point source reflections from a semi-infinite plane, parallel planes of a channel and a three dimensional cavity. The application of these models to compute the time-domain response in a cavity is presented.