A numerical model is proposed to predict the reverberant sound field in a system of two coupled volumes that are connected through an open aperture. The model is based on the numerical implementation of a diffusion model that has already been applied to predict the sound-energy distribution and the sound decay in single rooms. In comparison with the statistical theory, the proposed approach permits the prediction of the sound field by taking into account the sound source location and the receiver locations as well as the transition from one room to the other at the coupling aperture. Moreover, the diffusion model results match satisfactorily the experimental data in terms of sound-pressure level and reverberation times, both in the room containing the source and in the receiving room. Simulations with a ray-based model are also carried out, leading to results similar to those of the diffusion model, but at a cost of larger computation times.

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This paper presents an extension of a diffusion model for room acoustics to handle the atmospheric attenuation. This phenomenon is critical at high frequencies and in large rooms to obtain correct acoustic predictions. An additional term is introduced in the diffusion equation as well as in the diffusion constant, in order to take the atmospheric attenuation into account. The modified diffusion model is then compared with the statistical theory and a cone-tracing software. Three typical room-acoustic configurations are investigated: a proportionate room, a long room and a flat room. The modified diffusion model agrees well with the statistical theory (when applicable, as in proportionate rooms) and with the cone-tracing software, both in terms of sound pressure levels and reverberation times.

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In this paper, a modification of the diffusion model for room acoustics is proposed to account for sound transmission between two rooms, a source room and an adjacent room, which are coupled through a partition wall. A system of two diffusion equations, one for each room, together with a set of two boundary conditions, one for the partition wall and one for the other walls of a room, is obtained and numerically solved. The modified diffusion model is validated by numerical comparisons with the statistical theory for several coupled-room configurations by varying the coupling area surface, the absorption coefficient of each room, and the volume of the adjacent room. An experimental comparison is also carried out for two coupled classrooms. The modified diffusion model results agree very well with both the statistical theory and the experimental data. The diffusion model can then be used as an alternative to the statistical theory, especially when the statistical theory is not applicable, that is, when the reverberant sound field is not diffuse. Moreover, the diffusion model allows the prediction of the spatial distribution of sound energy within each coupled room, while the statistical theory gives only one sound level for each room.