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Computer-Aided Calculation of the Reverberation Time

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An almost obvious and relatively simple approach for deriving the reverberation time from computed values of Mean Free Path (MFP) and Mean Sound Absorption (MSA) in an enclosure is described. Calculation of MFP and MSA is based on computer simulation of sound propagation in the room utilizing ray-tracing technique. Thus, the dependence of reverberation time on room shape and distribution of the sound-absorbing materials in the hall is taken into account. The free path, which sound rays travel between two reflections, and sound absorption coefficient they encounter on each reflection, are considered random variables. The mathematical expectations of those variables MFP and MSA are evaluated from corresponding empirically found probability distributions, termed frequency distributions. Thus, MFP is computed as average value of thousands of free paths, observed during the ray-tracing simulation. A special history of incident transfer between surfaces or HITS-table is used to determine MSA coefficient. MSA is calculated as average of weighted absorption coefficients of the room boundaries. Each weight is proportional to computed probability of hitting respective surface by the sound rays. A model of a concert hall is studied and computed reverberation time is compared to the measurements and calculations using traditional formulae.

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