A NUMERICAL AND EXPERIMENTAL VALIDATION OF THE DIFFUSION EQUATION APPLIED TO ROOM ACOUSTICS

The recently developed room-acoustics diffusion model relies on the basic as- sumptions of the Fick’s law of diffusion, relating the acoustic intensity and the energy density inside a room, through a constant diffusion coefficient. This study investigates the relationship between these two acoustic quantities in the station- ary state, for the particular case of long rooms with different amounts of boundary scattering, by means of numerical simulations and experimental measurements. The numerical study was performed with a sound particle-tracing code. The ex- periments consist in measurements inside the scale model of a long room, where a three-dimensional Microflown➤ probe (calibrated and equalized with digital filters) was employed to collect data in terms of pressure and axial velocity components. Then, for each receiver position, the intensity and the energy density gradient were derived. Both numerical and experimental results show that inside long rooms the diffusion coefficient is not a constant but increases with the distance from the source, with a slope depending on the scattering coefficient of the walls. This re- sult implies that, for such long enclosures, the diffusion model should consider a space-varying diffusion coefficient to be more consistent with real phenomena.