Characterization of a diffuse field in a reverberant room

An efficient modal approach to characterize the diffuseness of the sound field in a rectangular room is presented. Using two simple descriptors, the correlation function and the spatial uniformity of the pressure field, a practical and convenient tool is proposed to study the diffuse field in the room. A precise criterion has been given in terms of the least permissible number of room modes to achieve an adequate diffusion. It has been shown that the criterion is in great accordance with the well-known “Schroeder frequency” limit for the diffuse field. Detailed calculations of the correlation function are presented to show the importance of the Δk/k correction terms to the well-known sin(kR)/kR prediction. A new closed form for the correlation function is thus derived. A discussion about the importance of having more than one descriptors is also presented. It is shown that a diffuse field can be established in a room with strong modal behavior under certain assumptions.