Transient chaos in room acoustics

The decay of sound in an auditorium due to absorption is central to the theory and practice of room acoustics. Within geometrical acoustics, this problem involves the partial trapping of chaotic ray trajectories in billiards, hence transient chaos. We first present a theoretical and numerical analysis of the decay of rays in 2-D chaotic billiards (2-D room acoustic models) and show that the existence of fluctuations (in the mean-free path and in the rate of phase space exploration) leads to modifications from the standard statistical theory. An ergodic wave theory of room acoustics based on a wave formulation is then discussed and tested by direct numerical calculations of the eigenmodes in 2-D billiards. Finally, we present a semiclassical calculation of the acoustic Green's functions in the time domain, based on a summation over rays, viewed as generalized wave impulses, and successfully compare its predictions with a direct numerical integration of the wave equation. This formalism provides a framework to link the geometrical ray description to the ergodic wave theory.