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Sound field behavior in performance spaces is a complex phenomenon. Issues regarding coupled spaces present additional concerns due to sound energy exchanges. Coupled volume concert halls have been of increasing interest in recent decades because this architectural principle offers the possibility to modify the hall's acoustical environment in a passive way by modifying the coupling area. Under specific conditions, the use of coupled reverberation chambers can provide non-exponential sound energy decay in the main room, resulting in both high clarity and long reverberation which are antagonistic parameters in a single volume room. Previous studies have proposed various sound energy decay models based on statistical acoustics and diffusion theory. Statistical acoustics assumes a perfectly uniform sound field within a given room whereas measurements show an attenuation of energy with increasing source-receiver distance. While previously proposed models based on diffusion theory use numerical solvers, the present study proposes a heuristic model of sound energy behavior based on an analytical solution of the commonly used diffusion equation and physically justified approximations. This model is validated by means of comparisons to scale model measurements and numerical geometrical acoustics simulations, both applied to the same simple concert hall geometry.

In Room Acoustics, the quantity that fully describes the hall is a set of room impulse responses (RIRs), which are composed of the succession of arrivals (i.e., some sound rays which have undergone one or more reflections on their way from the source to the receiver). The mixing time is defined as the time it takes for initially adjacent sound rays to spread uniformly across the room. This paper proposes to investigate the temporal distribution of arrivals and the estimation of mixing time. A method based on maxima of correlations (Matching Pursuit) between the source impulse and the RIR allows to estimate in practice arrivals. This paper compares the cumulative distribution function of arrivals of experimental and synthesized RIRs (using a stochastic model). The mixing time is estimated when the arrival density becomes constant. The dependance of mixing time upon the distance source/receiver is investigated with measured and synthesized RIRs.

Compared with more fashionable computer modeling, acoustical modeling is far from being superseded. In fact, there is often no alternative to acoustical modeling when designing an auditorium. Careful analysis of the laws of similarity shows that there remains some possibility of improving the acoustical testing of small models. This improvement does not solely concern transducers but the processing of impulse responses as well. Digital processing provides both accuracy of computation and compensation for air attenuation. Based on these principles, a computer-aided testing plant was designed and a computer package was written to drive it. A modular structure was selected as giving the maximum flexibility. Thus a digital evaluation of objective room-acoustical parameters can be achieved within a few minutes. So far, computer-aided acoustical modeling has proved well adapted for research and designing purposes.

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