Complex resonance frequencies numerically obtained in the rectangular room with arbitrary wall impedances

Abstract

Numerical methods to finding the complex resonance frequencies in the rectangular room with arbitrary wall impedances are presented. The eigenvalue equation is written in such a way that allows the unambiguous identification of each Riemann sheet. One numerical procedure applies the Newton method. For each wall-pair mode, the complex resonance frequencies are found, in each Riemann sheet, by small perturbations to the impedances of the wall pair. Another procedure transforms the eigenvalue equation into two differential equations, which are numerically integrated by the homotopic continuation procedure. The latter procedure is faster and finds all possible solutions. From the knowledge of sound decays experimentally obtained in a hard walled rectangular room, the impedances of the hard walls are obtained, which are then used to predict sound decays in the same room with one surface lined with sound absorbing material. It is shown that groups of modes with different reverberation times may collectively produce sound decays not always consistent with the Sabine prediction, and with some experimental results in a rectangular room with the floor covered with sound absorbing material of known acoustic impedance.