Sound field modeling in streets with a diffusion equation

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Abstract
By assuming that the surface irregularities of the building facades are adequate to produce diffusion in streets, a diffuse sound field model using the mathematical theory of diffusion is used to predict the sound propagation and its reverberation in rectangular streets. This model, developed to predict the sound field in rooms with diffusely reflecting boundaries, is applied in this paper to urban acoustics. A 3D diffusion equation is derived for the sound energy density and solved for time-varying sources and in steady state. A diffusion parameter is introduced to characterize the amount of diffusion in the street. An exchange coefficient depending on the absorption coefficient is also used to take into account the wall absorption. When the diffusion coefficient is rightly chosen, the predicted reverberation times and sound attenuations are in accordance with measurements in a scale model of a street.

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