Revision of Sabine's and Eyring's reverberation theories

Sabine's and Eyring's reverberation theories are still the most important theoretical frameworks for room acoustics. The important physical quantities derived from these theories are the average sound pressure level (sound energy density) and the reverberation time (sound energy decay). Eyring revised Sabine's theory to become the reverberation time zero in the perfect absorption condition. However, Eyring's theory has contradictions regarding the sound energy density in a steady state and the energy decay from the steady state. In this study, in order to resolve these contradictions, the theoretical framework for the consistent system is presented introducing the new concept of the average impulse response in a room, and the contradictions in the current room acoustic theory are clarified. Based on the theoretical framework, Sabine's reverberation theory is revised by a different way of Eyring's theory. The reverberation time of the revised theory is shorter than that of Sabine's theory and longer than that of Eyring's theory. Finally, ray-tracing computer simulations were performed to verify the revised theory. Results of sound ray tracing simulations were in better agreement with the values calculated using the revised theory rather than those calculated using Sabine's and Eyring's theories.