Confirming dimensional reduction assumptions for the energy-stress tensor through comparison with high-frequency wave-based pressure simulations
Résumé
In room acoustics, the energy-stress tensor represents the conservative relationships between the acoustic energy density, sound intensity, and the symmetric wave-stress tensor. In real rooms, the off-diagonal components of the wave-stress tensor are non-zero, implying the existence of shear stresses acting upon the energetic quantities. Assumptions regarding these terms in 1- and 2-dimensional spaces [Dujourdy et al. 2017, 2019] were used to reduce the energy-stress tensor relationships to a tractable system capable of predicting frequency- dependent stochastic reverberation decays in those spaces [Meacham et al. 2019]. Direct verification of those assumptions at a single location in a real space would require more measurements at varying positions than can be reliably captured without robotization, let alone in acoustically distinct regions of a room. Therefore, in this work, we aim to verify the 1-dimensional reduction assumptions by examining a high- frequency wave-based pressure simulation, allowing averaging over a wide number of sampling positions at multiple locations throughout a space, providing insight into the relationship between room geometry and the terms of the energy-stress tensor.
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