Theoretical and numerical studies of low-frequency reverberant sound field in coupled rooms

The paper examines the low-frequency reverberation sound field in coupled-room systems. In theoretical model, the modal expansion of sound pressure was applied, while in numerical procedure, the discrete Hilbert transform was used to determine the amplitude of decaying sound. Computer simulations were performed for a room system consisting of two connected rectangular rooms. Eigenfunctions and eigenfrequencies of this system were determined by the finite element method. Simulation results showed that for the hard-walled room system the sound decay is almost exponential for frequencies of modes localized in one of the subrooms. Acoustical treatment of the ceiling significantly reduced reverberation. However, due to beating effects and modal overlap, a large irregularity of sound decay curves has occurred. This makes it difficult to correctly qualify the sound decay, because in this case it is practically impossible to characterize the reverberation process with only one or at most two decay times.