The diffusion coefficient D Fick increases as a function of the position X, the absorption α, and the cross section of the corridor S c. Conversely, when the wall absorption increases, the diffusion process is non-homogeneous. 3 showed that the diffusion coefficient D Fick varies weakly with space and that the expression proposed in Eq. For the case of weakly absorbent corridors, Visentin et al. In this work, the estimation of D Fick ( X ) using the Fick's law was considered as a numerical “measurement” of the diffusion coefficient variation. It has been shown that the diffusion coefficient is proportional to the speed of sound c and the mean free path λ ( r ) as 2 The accuracy of room-acoustic predictions depends on the diffusion coefficient, possibly spatially varying and denoted D ( r ). In this modeling framework, the acoustic energy density w ( r ), corresponding to the number of sound particles in an elementary volume centered at r (the space variable), is governed by a diffusion equation, associated with the “Fick's law,” expressing the proportionality between the intensity I ( r ) and the energy density gradient ∇ w ( r ). 1 This propagation is assumed to be similar to that of particles propagating through an equivalent volumetric scattering medium made of targets by multiple collisions (such as light propagation through fog). The acoustic diffusion model is based on the hypothesis that the reverberant sound field can be seen as a set of sound particles of elementary energy propagating along straight lines between two successive collisions with the walls. Acoustics predictions of reverberation in rooms with large aspect ratios turn out to be erroneous if the inhomogeneity of diffusion is not taken into account. 3 The diffusion coefficient increases with the distance to the sound source and also according to the wall absorption and room aspect ratio, involving an inhomogeneous diffusion process. However, this last expression is not valid in the case of elongated rooms, as has been shown from the Fick's law based on acoustic energy density and intensity. Currently, this mean free path is chosen to be equal to the mean free path of the room, which involves a homogeneous diffusion process (constant diffusion coefficient). In the original theory, 2 this diffusion coefficient can be spatially dependent due to its proportionality to the mean free path, which can vary spatially and can be expressed as the distance travelled by the particles without collisions with targets weighted by a non-collision probability. 1 The acoustic energy density, corresponding to the number of sound particles in an elementary volume, is then assumed to be governed by a diffusion equation, a key factor being a diffusion coefficient accounting for the impact of the room on the diffusion process. For several years now, the original theory of diffusion, modeling the propagation of diffusing particles through scattering targets (presumed infinite medium), has been adapted to the case of room acoustics (acoustic diffusion model for a closed environment). Assuming that the sound field can be seen as a set of elementary energy sound particles propagating at the speed of sound, this work concerns the study of the dynamics of these particles when the room under study is of elongated shape.
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