Calibrating the Sabine and Eyring formulas

Funding Information: This work was supported by the Nordic Sound and Music Computing Network—NordicSMC, NordForsk Project No. 86892. Publisher Copyright: © 2022 Author(s).Of the many available reverberation time prediction formulas, Sabine's and Eyring's equations are still widely used. The assumptions of homogeneity and isotropy of sound energy during the decay associated with those models are usually recognized as a reason for lack of agreement between predictions and measurements. At the same time, the inaccuracy in the estimation of the sound-absorption coefficient adds to the uncertainty of calculations. This paper shows that the error of incorrectly assumed sound absorption is more detrimental to the prediction precision than the inherent error in the formulas themselves. The proposed absorption calibration procedure reduces the differences between the measured and predicted reverberation time values, showing that an accuracy within ±10% from the target reverberation time values can be achieved regardless of the absorption distribution in a room. The paper also discusses the oft neglected air absorption of sound, which may introduce considerable bias to the measurement results. The need for an air-absorption compensation procedure is highlighted, and a method for the estimation of its parameters in octave bands is proposed and compared with other approaches. The results of this study provide justification for the use of the Sabine and Eyring formulas for reverberation time predictions.Peer reviewe

Distribution of Modal Damping in Absorptive Shoebox Rooms

Funding Information: The work of M. Schäfer was supported by the Bavarian State Ministry of Science and Arts within the bidt Graduate Center for Postdocs. Publisher Copyright: © 2023 IEEE.The image-source method is widely applied to compute room impulse responses (RIRs) of shoebox rooms with arbitrary damping. However, with increasing RIR lengths, the number of image sources grows rapidly, leading to slow computation. We propose a method to estimate the damping density of a damped shoebox room, which in turn can provide the energy decay necessary to model the stochastic late reverberation. The damping density is derived from a modal decomposition that is compliant with the ISM solution. We show that the proposed method gives a more accurate estimate of the energy decay than previous methods and can be efficiently computed regardless of the RIR lengths. While we focus on the derivation and evaluation, the main practical applications of the proposed model include, e.g., the faster synthesis of late reverb and the analysis of multi-slope decays.Peer reviewe