In room acoustics, the mean-free path λ of the room is evaluated by:

(8–236)

where:

According to the theory of diffusion for particles in a scattering medium, the diffusion coefficient of a room is defined as:

(8–237)

where:

The acoustic energy density flux is defined by the gradient of energy density as:

(8–238)

The acoustic diffusion model is governed by the following diffusion equation:

(8–239)

where:

Dt = the total diffusion coefficient in the room, which is defined by the diffusion coefficient De in the empty room and the diffusion coefficient of the furniture Df in the room:

ma = coefficient of atmospheric attenuation

αf = absorption coefficient of furniture in the room

λf = mean-free path of furniture in the room, which is calculated by the number of furniture items per unit volume nf and the furniture’s average scattering-section Qf:

= omnidirectional radiated sound power source

The weak form of the acoustic diffusion model is cast by:

(8–240)

The energy exchange on the boundaries in the acoustic diffusion model is described by the mixed boundary condition:

(8–241)

where:

h = exchange coefficient, which is calculated as:

= outward normal unit vector of the surface

The acoustic energy exchanges transferring from one room to another through a partition wall with coupled area S₁₂ in the room 1 and S₂₁ in the room 2 are described by the following:

(8–242)

where:

= transmission coefficient, which is calculated by the transmission loss R(dB); that is = 10-R/10

A two-port network admittance matrix is implemented to couple two rooms together (see Transfer Admittance Matrix for more information on the transfer admittance matrix):

(8–243)