Revision of Sabine's reverberation theory by following a different approach to Eyring's theory

Abstract

The room acoustic theory was established based on Sabine's reverberation theory. However, in Sabine's theory, the reverberation time does not reach zero, even if the absolute absorption condition is satisfied. This is a contradiction of Sabine's theory, and Eyring revised the reverberation theory to resolve this contradiction. In this paper, a theoretical framework for the consistent reverberation theory is presented. Using this framework, it was demonstrated that Eyring's theory has a contradiction between the sound energy density in the steady state and energy decay from the steady state, which is absent in Sabine's theory. Based on the proposed theoretical framework, Sabine's reverberation theory was revised using an approach that is different from that of Eyring. The reverberation time obtained using the revised theory was shorter than that obtained using Sabine's theory and longer than that obtained using Eyring's 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.

arXiv comment[V2] This version was added detailed explanation of the theory and some new results. 7 pages, 3 figures, 1 table [V3] Detailed explanations of the revised reverberation theory, especially the mean absorption free path, and some new simulation results related to it have been added [V4] The explanations for the reverberation of direct sound in the revised theory have been added to Section 4.1