Theoretical model on reverberation decay in a rectangular room with specular reflective walls

Reverberation is the most important consideration when designing sound field in a room. Reverberation energy decay of diffuse sound field is exponential. The reverberation time characterizes a decay rate in the condition where the decay is exponential. However, it is known that a non-exponential energy decay occurs in a room with unevenly distributed sound absorption, namely non-diffuse sound field. The reverberation cannot be defined in such sound field with non-exponential decay. In the present paper, we propose theoretical model on reverberation decay in non-diffuse sound fields. The reverberation decay is usually characterized by absorption and scattering properties of surfaces of a room. As a first step for developing reverberation theory of non-diffuse sound field, the proposed model deals with rectangular rooms with specular reflective walls. Rectangular rooms are very common in any kind of buildings and architecture. Spatial absorption coefficients for three orthogonal directions are defined as important parameters which characterize the energy decay curve in the rectangular room. By using the model the reverberation in such rectangular room becomes a combination of exponential decay and power law decay. The power law as a function of time includes a problem of infinity. This model solves the problem. This model was verified by comparing with results of computer simulation, sound ray tracing method. Theoretical solutions of the proposed model corresponded well with the results of the computer simulation.