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Transient chaos in room acoustics
Fabrice Mortessagne1, Olivier Legrand, Didier Sornette
1Laboratoire de Physique de la Matiere Condensee, CNRS URA 190 Faculte des Sciences, Parc Valrose, 06108 Nice Cedex 02, France.
Chaos (Woodbury, N.Y.)
|October 1, 1993
Summary
Sound decay in auditoriums is modeled using chaotic ray trajectories in billiards. Fluctuations modify standard theories, bridging geometrical acoustics and wave theory for better room acoustics predictions.
Area of Science:
- Room acoustics
- Theoretical physics
- Acoustics
Background:
- Sound decay in auditoriums is crucial for room acoustics.
- Geometrical acoustics models sound using chaotic ray trajectories.
- Transient chaos arises from ray trapping in billiards.
Purpose of the Study:
- Analyze sound decay in 2-D chaotic billiards.
- Investigate modifications to statistical theory due to fluctuations.
- Develop a framework linking geometrical and wave theories.
Main Methods:
- Theoretical and numerical analysis of ray decay in 2-D billiards.
- Ergodic wave theory formulation and numerical testing.
- Semiclassical calculation of acoustic Green's functions.
Main Results:
- Fluctuations in mean-free path and phase space exploration alter standard statistical theory.
- Numerical calculations validate ergodic wave theory.
- Semiclassical method successfully predicts wave equation behavior.
Conclusions:
- A unified framework connects geometrical ray descriptions with ergodic wave theory.
- Transient chaos and fluctuations significantly impact sound decay models.
- The study advances the understanding of sound propagation and decay in enclosed spaces.