Sound energy decay in coupled spaces using a parametric analytical solution of a diffusion equation

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.