Solid-angle based reverberation time estimation for rooms with substantial “early absorption”

Parametric design tools allow for rapid design evaluation of geometric options for an auditorium early in the design process. A key design parameter is the required room volume to obtain a design reverberation time. While initial volumetric requirements can be obtained using existing methods (e.g., Sabine equation), the accuracy is reduced for “early absorptive” rooms where a significant proportion of the incident sound goes onto absorptive surfaces either directly or after a strong early reflection, e.g., auditoria with steep seating rakes and “directed reflection sequence” rooms with strong early reflections. In these rooms, the solid angle over which sound is incident on absorptive surfaces is large, and the volumetric requirement is often underestimated. Often, it is only when the room is modeled computationally that a shortfall in the room volume is identified. A more reliable method is needed, using geometrical parameters such as solid angles that can be obtained from parametric tools. A new formula for estimating reverberation time considering this “early absorptive” solid angle is proposed. The results are compared to traditional statistical formulae and Odeon simulations. The new formula provides an improvement to existing formulae for “early absorptive” rooms. Potential modifications to incorporate source directivity and scattering are discussed.