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

Abstract

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.

An Influence of the Wall Acoustic Impedance on the Room Acoustics. The Exact Solution

“…(11) in the z-direction, with boundary conditions Eqs. (25) and (26). The general solution takes the form, cf.…”

“…They use statistical-acoustic methods (Summers, 2012), the diffusion-equation model (Luizard et al, 2014), geometric acoustics methods (Luizard et al, 2014;Lehmann, Johansson, 2008), the combination of radiosity method, geometrical acoustic one (Korany et al, 2001), and so on.…”

Investigation of the effective aperture area of sliding and hinged doors between coupled spaces

“…15 Acoustical parameters were obtained in the present study from analysis of the measured impulse responses using the Marching Line analysis method. 12,14 The decay curve quantifiers are the decay time (DT i ) of each slope within the curved decay, evaluated over 60 dB, and the time and level (BP ti and BP Li ) of the point on the decay curve between consecutive slopes, called the bending point, as illustrated in Fig. 2(A).…”

“…Recent studies have also examined the ability of different numerical methods to model coupled volume acoustics. 11,12 The present study first intends to quantify the differences observed between coupling system designs comparing sliding and hinged or rotating doors. Recorded impulse responses using a scale model are analyzed and acoustical parameter variations are compared, providing an equivalent aperture in terms of open angle for the rotating door as compared to the aperture area as a function of open width for the sliding door.…”

Prediction of Reverberant Properties of Enclosures via a Method Employing a Modal Representation of the Room Impulse Response

“…Statistical-acoustic methods (Summers et al, 2004;Summers, 2012) are based on the diffuse sound field hypothesis that the acoustic energy is uniform in the field and travels in all directions with the same probability. The diffusion-equation model (Xiang et al, 2009;Luizard et al, 2014) is an extension of the statistical theory to spatially varying reverberant sound fields and is based on the analogy of the sound energy density with a density of "sound particles" travelling along straight lines. The geometric acoustics methods are adequate for high sound frequencies and most systems for geometric modelling are based on the ray tracing method (Summers et al, 2005), the beam tracing algorithm (Funkhouser et al, 2004;Laine et al, 2009), the image source method (Dance et al, 1995;Lehmann, Johansson, 2009), or the mirror source method (Mechel, 2002;Aretz et al, 2014).…”