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

TL;DR

This paper revises Sabine's reverberation theory by proposing a new theoretical framework, addressing contradictions in Eyring's revision, and demonstrating improved accuracy through sound ray tracing simulations.

Contribution

A new theoretical framework for reverberation time that resolves contradictions in existing theories and improves agreement with simulation results.

Findings

Revised reverberation time is between Sabine's and Eyring's predictions.

Sound ray tracing results align better with the revised theory.

Identifies contradictions in Eyring's theory between energy density and decay.

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.