Mixing time measurement in Sabinian and non Sabinian rooms

The room impulse response of a reverberant space is composed of three elements: the direct sound, early reflections and diffuse reverberation. The study and analysis of these elements allows the time domain description of an acoustic space. The goal of this work is to extrapolate from the impulse response information regarding the way in which the transition between the early reflections deterministic section and the stochastic diffuse field occurs. The time instant that identifies this transition is called mixing time. This parameter, whose theoretical value is given by the square root of the room volume, allows us to understand the moment from which it will be possible to consider the sound field diffuse and the acoustic energy uniformly distributed inside the space. Two different methods to study the statistical properties of impulse responses were found in scientific literature, measuring the way in which the density of reflections increases as time passes, until the moment when the whole process can be considered Gaussian. Appropriate changes to the proposed methodologies are implemented: developed algorithms have been tested on a variety of impulse responses measured in six environments different for dimensions, sound absorption characteristics and utilization. Particular attention is given to non-Sabinian environments, room with small dimensions and heavy sound absorption, in which Sabine's assumptions about diffuse sound field cannot be considered fulfilled. The obtained results show how theoretical value of mixing time constitutes an approximation of measured value only for Sabinian rooms, while for non-Sabinian spaces, in which the parameter is still measurable, the measured value diverges considerably from the theoretical one. It has been also demonstrated experimentally the relationship between sound diffusion and mixing time, showing how the presence of scattering elements within an acoustic space contributes to lower the mixing time.