Analysis of Sabine and Eyring equations and their application to concert hall audience and chair absorption

Abstract

Historically, two equations have been used for predicting reverberation times, Sabine and Eyring. A precise means is presented for determining Eyring absorption coefficients alpha(eyring) when the Sabine coefficients alpha(sabine) are known, and vice versa. Thus, either formula can be used provided the absorption coefficients for the Sabine formula are allowed to exceed 1.0. The Sabine formula is not an approximation to the Eyring equation and is not a shortcoming. Given low reverberation times, the ratio of alpha(sabine) to alpha(eyring) may become greater than 2.0. It is vital that, for correct prediction of reverberation times, the absorption coefficients used in either formula must have been determined in spaces similar in size and shape, with similar locations of high absorption (audience) areas, and with similar reverberation times. For concert halls, it is found that, when the audience area (fully occupied) and midfrequency reverberation time are postulated, the hall volume is directly proportional to the audience absorption coefficient. Approximately 6% greater room volumes are needed when choosing nonrectangular versus classical-rectangular shaped halls and approximately 10% greater volumes when choosing heavily upholstered versus medium upholstered chairs. Determinations of audience sound absorption coefficients are presented, based on published acoustical and architectural data for 20 halls.