Lower bound on frequency validity of energy-stress tensor based diffuse sound field model

A lower bound on the frequency validity limit is established for an energetic wave equation derived from the energy-stress tensor, examined in the one-dimensional case [Dujourdy et al, Acta Acustica united with Acustica 103:480-491, 2017]. The method efficiently models diffuse sound fields that dominate reverberation at higher frequencies and larger distances. Initially noted in the course of an exhaustive search of the solution space of all valid model parameters, the low-frequency cutoff has implications for the utility of the method in a hybridization context. In practice, the bound is encountered when determining the absorption and diffusion coefficients by iteratively approaching the temporal and spatial decay of measured data. As the test frequency decreases, the ranges of coefficient combinations that result in less than 10% variation from each decay measure can diverge until the region where both measures are satisfactory (the intersection of the two domains) disappears. Further evidence for the bound is provided through comparison with measurements of a long hallway, and stability concerns in the cases where both coefficients are very small are addressed.