A review of mixing time estimators.

Abstract

In 1967, Joyce introduced the concept of dynamical systems in the room acoustics community. Based on statistical physics from the early 20th century, Joyce assumed large halls to be ergodic and mixing. Since that time, the hypothesis of mixing rooms has been accepted, but only a few studies have focused on the experimental validation of such an assumption. In 1982, Polack proposed a heuristic formulation of the mixing time, based on perceptual criteria. After that time, the sound field is, theoretically, uniform throughout the room, i.e., the density of sound rays must be homogeneous and isotropic at any time in the phase space. Many acousticians have related the mixing time to the beginning of the diffuse sound field, also called the late reverberation. In a recent work, we have investigated two different approaches for experimentally estimating the mixing time from measured impulse responses. We present these two estimators and explain our results. In particular, we show that the relationship between mixing and late reverberation is not straightforward. Finally, we conclude that mixing may occur later after the beginning of late reverberation. Consequently, instead of mixing time, we propose the term of cross‐over time.