A systematic study of power-law decays in reverberation rooms

A space-ensemble average decay curve 〈S2 (t) 〉NO, obtained in a reverberation room, shows a smooth but notable curvature at low frequencies, implying a lack of diffusion. It is closely approximated by L (t), the theoretical curve for power-law decays given by Schroeder 5th ICA, paper G31 (1965), and can be quantitatively characterized by only two parameters for L (t), i. e. , by T0 (initial decay time) and Q30 (curvature index). This allows a quantitative evaluation of the diffusion condition in the decay process, always relating it to the absorption coefficient (αrev) evaluated from the identical 〈S2 (t) 〉NO. The validity of 〈S2 (t) 〉NO has been verified by its application in the design of a large-scale reverberation room (570 m3) provided with a huge rotating vane (6 m in diameter) on the ceiling. A large contribution of the vane to the linearization of 〈S2 (t) 〉NO, and hence, to the increase in measured αrev has been clearly established after the construction. Theoretical analysis of the effectiveness of the vane has revealed that a lack of diffusion positively bends 〈S2 (t) NO without affecting the initial decay rate. Accordingly, the conventional reverberation time T5-35 increases with the curvature Q30, inducing a negative systematic error in the αrev measurement, while T0 is almost fixed to the value for perfect diffusion, greatly reducing the error and scatter. The Q30 notation could be used for the qualification of reverberation rooms, since it refers to the diffusivity of the room itself, not of a certain specified point in it.