In this paper, the modal expansion method supported by a computer implementation has been used to predict steady-state distributions of the potential and kinetic energy densities, and the active and reactive sound intensities inside two coupled enclosures. The numerical study was dedicated to low-frequency room responses. Calculation results have shown that the distribution of energetic quantities in coupled spaces is strongly influenced by the modal localization. Appropriate descriptors of the localization effect were introduced to identify localized modes. As was evidenced by numerical data, the characteristic objects in the active intensity field are vortices positioned irregularly inside the room. It was found that vortex centers lie exactly on the lines corresponding to zeros of the eigenfunction for a dominant mode. Finally, an impact of the wall impedance on the quantitative relationship between the active and reactive intensities was analyzed and it was concluded that for very small sound damping the behavior of the sound intensity inside the room space is essentially only oscillatory.

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Abstract:The acoustical properties of an irregularly shaped room consisting of two connected rectangular subrooms were studied. An eigenmode method supported by a numerical implementation has been used to predict acoustic characteristics of the coupled system, such as the distribution of the sound pressure in steady-state and the reverberation time. In the theoretical model a low-frequency limit was considered. In this case the eigenmodes are lightly damped, thus they were approximated by normal acoustic modes of a hard-walled room. The eigenfunctions and eigenfrequencies were computed numerically via application of a forced oscillator method with a finite difference algorithm. The influence of coupling between subrooms on acoustic parameters of the enclosure was demonstrated in numerical simulations where different distributions of absorbing materials on the walls of the subrooms and various positions of the sound source were assumed. Calculation results have shown that for large differences in the absorption coefficient in the subrooms the effect of modal localization contributes to peaks of RMS pressure in steady-state and a large increase in the reverberation time.