A simplified method to estimate the free path length variance

Abstract

Kutruff derived an analytical solution for the prediction of reverberation time in spaces with arbitrary shape. It is the most popular analytical equation that contains shape factors. However, in this equation the free path length variance remains as unknown parameter. Kutruff suggested the implementation of Monte-Carlo simulation to determine this value for each unique shape. In practice this method is not significantly simpler than a full ray tracing simulation. Fortunately, using methods from the probability field, the free path length variance does have an analytical solution, but this takes such a complicated form that it is not convenient to use. This article treats the development of a simplified method to estimate the free path length variance without losing accuracy when applied to concert halls. A simplified regression model is developed for rectangular shapes based on the analytical solution. This simple model explains 99.8% variance for any rectangular shape up to 1:10:10. Secondly, for arbitrary shapes, a simplified model is proposed by including several additional simple variables. This model is validated against simulation results. It will be shown that this simplified method not only can be used in Kutruff’s equation, but also reveals the significant shape-related parameters that influence the reverberation time.