Sound absorption in concert halls: Rectangular versus other shapes; Sabine versus Eyring equations

Abstract

The accurate calculation of reverberation time in a concert hall in advance of construction is vital because it relates directly to the volume of the hall, a critical architectural parameter. The calculation can be by either the Sabine or Eyring equations which, broadly speaking, requires two quantities, the absorption coefficients of the seated audience plus orchestra and those of the nonaudience areas, i.e., side walls, ceiling, and the like. The two formulas require different sizes of absorption coefficients. The Sabine and Eyring equations are analyzed here, including their relative accuracies. A means for deriving the Eyring absorption coefficients when the Sabine coefficients are known is presented. Based on published acoustical and architectural data for 20 selected concert halls, which are of two shapes, the audience and chair absorption coefficients are calculated. It is concluded that for the same audience area and a given midfrequency reverberation time the volume of a hall is directly proportional to the midfrequency audience absorption coefficient, which, in turn depends on the type of chair and the shape of the hall. New audience absorption coefficients for medium and heavily upholstered chairs and for the two types of hall are presented.