An experimental analysis of the relationship between reverberant acoustic intensity and energy density inside long rooms

The recently developed room-acoustics diffusion model relies on the basic assumption 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 stationary state, for the particular case of long rooms with different amounts of boundary scattering, by means of experimental measurements. The experiments consist in measurements inside the scale model of a long room, where a three-dimensional Microflown probe (calibrated 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. The 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 result implies that, for such long enclosures, the diffusion model should consider a space-varying diffusion coefficient to be more consistent with real phenomena.