Fabrice Mortessagne
Olivier Legrand
Didier Sornette
Lab. de Phys. de la Matiere Condensee, CNRS URA 190, Faculte des Sci., Parc Valrose, B.P. 70, 06108 Nice Cedex 02, France
The theoretical validity of Sabine's law of reverberation in the true geometrical acoustic limit (TGAL) with mirror reflection relies solely on the conditions that almost all rays are chaotic and that absorption is ``sufficiently weak,'' as demonstrated by Joyce [J. Acoust. Soc. Am. 58, 643 (1975)]. It is shown here that exponential decay law may still hold in the TGAL for realistic large absorptions, depending on the spatial distribution of the absorption within the chaotic room. This dependence stems from the role of special ray trajectories that are analyzed. It is also demonstrated theoretically and numerically that Sabine's reverberation time is modified at large absorptions due to fluctuations in the number of encounters with the absorbing walls. This novel mechanism applies to many physical examples where a system decays from an initial metastable state with a generic exponential decay law, be it thermally activated or by quantum tunneling. A partial account of this work appeared in Europhys. Lett. 20, 287--293 (1992). Finally, a wave theory is given of Sabine's law for room acoustics relying on ergodic properties of the eigenmodes. Besides the global problem of reverberation, wave acoustics in ergodic rooms offer a true richness of phenomena that can be tackled with the help of tools developed in ``Quantrum Chaos.'' A preliminary account of this work appeared in Lect. Notes Phys. 392, 267 (1991).