Playing billiards in the concert hall: The mathematical foundations of geometrical room acoustics

Polack, Jean‐Dominique

doi:10.1016/0003-682x(93)90054-a

Cited by 59 publications

(35 citation statements)

References 7 publications

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“…In room acoustics, a room with positive Lyapunov exponents is chaotic, and is always ergodic and diffuse. 23,24 Thus, the SS system with positive k 1 has ray instability and may need a short time to reach the diffuse sound field.…”

Section: Numerical Calculations and Discussionmentioning

confidence: 99%

Ray chaos in an architectural acoustic semi-stadium system

2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The semi-stadium system is composed of a semicircular cap and a rectilinear platform. In this study, a dynamic model of the side, position, and angle variables is applied to investigate the acoustic ray chaos of the architectural semi-stadium system. The Lyapunov exponent is calculated in order to quantitatively describe ray instability. The model can be reduced to the semi-circular and rectilinear platform systems when the rectilinear length is sufficiently small and large. The quasi-rectilinear platform and the semicircular systems both produce regular trajectories with the maximal Lyapunov exponent approaching zero. Ray localizations, such as flutter-echo and sound focusing, are found in these two systems. However, the semi-stadium system produces chaotic ray behaviors with positive Lyapunov exponents and reduces ray localizations. Furthermore, as the rectilinear length increases, the scaling laws of the Lyapunov exponent of the semi-stadium system are revealed and compared with those of the stadium system. The results suggest the potential application of the proposed model to simulate chaotic dynamics of acoustic ray in architectural enclosed systems.

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Section: Numerical Calculations and Discussionmentioning

confidence: 99%

Ray chaos in an architectural acoustic semi-stadium system

2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Late reflections that arrive after the mixing time (t mix = √ V = 7.0 ms) are excluded with a time window. The mixing time has been proposed as a criterion that separates early reflections from late reflections [46][47][48]. Figure 4 shows the beam-power distributions of the desired and the reproduced fields when the reflection coefficient is 0.9.…”

Section: Properties Of the Beam-power Errormentioning

confidence: 99%

A Measure Based on Beamforming Power for Evaluation of Sound Field Reproduction Performance

Chang

Jeong

2017

Applied Sciences

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This paper proposes a measure to evaluate sound field reproduction systems with an array of loudspeakers. The spatially-averaged squared error of the sound pressure between the desired and the reproduced field, namely the spatial error, has been widely used, which has considerable problems in two conditions. First, in non-anechoic conditions, room reflections substantially deteriorate the spatial error, although these room reflections affect human localization to a lesser degree. Second, for 2.5-dimensional reproduction of spherical waves, the spatial error increases consistently due to the difference in the amplitude decay rate, whereas the degradation of human localization performance is limited. The measure proposed in this study is based on the beamforming powers of the desired and the reproduced fields. Simulation and experimental results show that the proposed measure is less sensitive to room reflections and the amplitude decay than the spatial error, which is likely to agree better with the human perception of source localization.

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“…For D er ¼ D 0 , the mixing time of a rectangular room can be derived, assuming c a ¼ 344 m=s, which yields t mix ¼ 0:9025 Â 10 À3 ffiffiffi ffi V p [22]. Table 1 gives the mixing time for different sizes of rooms.…”

Section: Multiple Reflections On Platementioning

confidence: 99%