Approximate theory of reverberation in rectangular rooms with specular and diffuse reflections

First, an approximate theory of reverberation in rectangular rooms is formulated as a specular reflection field based on the image source method. In the formulation, image sources are divided into axial, tangential, and oblique groups, which chiefly contribute to the corresponding groups of normal modes in wave acoustics. Consequently, the total energy decay consists of seven kinds of exponential decay curves. Second, considering surface scattering on walls with scattering coefficients, an integrated reverberation theory for nondiffuse field is developed, where the total field is divided into specular and diffuse reflection fields. The specular reflection field is simply formulated by substituting specular absorption coefficients, while the diffuse reflection field is assumed to be a perfectly diffuse field, of which energy is supplied from the specular reflection field at each reflection. Finally, a theoretical case study demonstrates how surface scattering affects the energy decay in rectangular rooms with changing the aspect ratio and the absorption distribution.