Role of the absorption distribution and generalization of exponential reverberation law in chaotic rooms

The theoretical validity of the classical 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)]. Recently it was shown that ‘‘sufficiently weak’’ may imply unrealistically large reverberation times [J. Acoust. Soc. Am. 88, 865 (1990)]. Here, this negative result is mitigated by showing that an exponential decay law may still hold in the TGAL for realistic absorptions, depending on the spatial distribution of the absorption within the chaotic room (for instance, in the case of uniform absorption on the walls). The dependence of the sound energy decay on the spatial distribution of absorption stems from the role of special ray trajectories which are analyzed. Also demonstrated theoretically and numerically is that the reverberation time is modified at large absorptions due to fluctuations in the number of encounters with the absorbing walls.