On the statistical properties of free path distribution as a means to investigate room acoustics of theatre halls

The free paths of reflections inside an enclosure can be viewed statistically as a distribution, whose mean is the well-known mean free path (MFP). Although the usage of the classical 4V/S formula to calculate MFP is familiar to most acousticians since long, the information embedded in the statistical distribution of free paths remains largely unexplored still today. Such distribution is now easily accessible thanks to CAD models that keep accurate track of reflections so that this function can be employed to test the peculiarities of geometry and material distributions. In this work the above framework was adopted to investigate how the sound field could be compared between different types of halls that were modeled with acoustical CAD. The analysis of free path distribution (FPD) was accomplished by means of higher order moments and especially using quantile plots to highlight the behavior of the reflections in the different halls compared to the most regular shapes. Several conclusions can be drawn relating the trend and the shape of the plots to hall's features, so that this approach seems quite promising to better describe the acoustical character of enclosures.