Reconstruction of the reverberation theory in a diffuse sound field by using reflection orders

TL;DR

This paper presents a new mathematical model for room reverberation based on reflection orders, reconciling and extending previous theories by incorporating the concept of reverberation of direct sound, with results aligning well with simulations.

Contribution

The paper introduces a novel reverberation model using reflection orders that revises existing theories and includes the temporal energy distribution of reflections.

Findings

Model aligns with previous revised theory

Good agreement with simulation results

Highlights importance of direct sound reverberation

Abstract

Room acoustics is mainly based on the reverberation theories of Saine and Eyring. In Sabine's theory however, the reverberation time does not reach zero, even if the condition of absolute absorption is fulfilled. Eyring revised reverberation theory to resolve this contradiction. However, Eyring's theory has an inconsistency between the formulations of the steady-state and decay processes. Therefore, the author revised Sabine's theory, taking a different approach from that of Eyring. This revised theory was constructed by introducing the concept of "reverberation of a direct sound." In this study, a new mathematical model of reverberation using reflection orders is proposed. This is a reconstruction of the author's revised theory. The new model includes the temporal energy distribution in each reflection order and uses the concept of "reverberation of a direct sound" for the entire reverberation process. It shows that the concept is also essential for the reflected sounds. In addition, the reverberation decay agrees with the revised theory previously proposed by the author. Overall, the new model showed good agreement with the simulation results.