Validation of a numerical diffusion equation-based modelling of the reverberated sound field in long rooms

Many applications as corridors, railways tunnels or tube stations present a long room geometry. A fast and reliable modelling of such sound fields could be helpful for designers. In fact, the classical statistical theory based on the assumptions of diffuse sound field is not applicable in such cases because the reverberant sound energy along the room is not uniform. In this study, several models assuming diffuse reflections of sound by walls are used for predicting the reverberant sound field in long rooms. Two models based on a diffusion equation for the energy density (one numerical and one analytical based on an image approach for describing the sound reflection at the corridor extremity) are compared with a radiosity model, and with a ray tracing software. Predictions are compared in terms of sound attenuation and reverberation time with measured data. The long rooms considered in this study were two rectangular corridors of lengths 20.3m and 47.3m.
All models overestimate the attenuation, reaching 6dB for the numerical diffusion based model. When a part of specular reflection (30%) is added in the ray tracing model, the predicted sound attenuation matches with the measured one: even in case of rough surfaces, specular reflections cannot be totally excluded.
For reverberation time, the agreement between predictions and experiments is good with fewer than 15% of discrepancy. The best predictions of the reverberation time were given by the diffusion models, with discrepancy less than 2% for the numerical model. So, it could be concluded that it is difficult to find a prediction method which is consistent both in terms of steady state and sound decay for the acoustics of long halls.