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

The room acoustics 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. Eyring revised the reverberation theory to resolve this contradiction. However, Eyring's theory is inconsistent in its formulation of the steady state and decay processes. Therefore, the author has revised Sabine's theory (Hanyu, Acoustical Science & Technology 45, 3, 2024), 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 paper, a new mathematical model of reverberation using reflection orders is proposed. This means that the revised theory already proposed by the author is reconstructed to include the temporal energy distributions in each reflection order. The new mathematical model also uses the concept of "reverberation of a direct sound" but describes the reverberation of only reflected sounds without the direct sound. This means that the concept of "reverberation of a direct sound" is essential also to the entire reverberation process. Reverberation decay of the new model is consistent with that of the already proposed revised theory. The new model showed good correspondence with the simulation results.