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

In this paper, the validity of the Fick's law of diffusion in room acoustics is experimentally investigated inside long rooms. The room-acoustics diffusion model relies on Fick's law stating a proportionality relationship between sound intensity and energy density gradient inside a room through a constant diffusion coefficient. This relationship is investigated in the stationary state for the particular case of long rooms with different amounts of boundary scattering. Measurements were performed inside a 1:16 scale model, using a p-u sound intensity probe (calibrated with digital filters) to collect concurrent data in terms of sound pressure and axial velocity components. Then for each receiver position, sound intensity and energy density gradient were derived. The 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. Numerical simulations of the enclosures were performed too by using a sound particle-tracing code; a substantial agreement with the experimental findings is observed. The results imply that for such long enclosures, the diffusion model should consider a space-varying diffusion coefficient to be more consistent with real phenomena.