Study Of Spatial Sound Field Using Ray Chaos Methods

Application of chaotic method in Hamiltonian system into various fields has been attacted more and more attention.The analysis of spatial sound field performance by using chaotic method provides more ideas for acoustic workers.Based on quantitative determination of chaotic systems,we use the largest Lyapunov exponents(LLEs)and the largest local Lyapunov exponents(LLLEs)to describe the acoustic ray movement.In this paper three-dimensional rectangular and concave spaces were established and the LLEs of ray systems were calculated;three-dimensional rectangle and Sinai space were established and the LLLEs of ray systems were calculated.According to ray-tracing algorithm,the paths along which the ray propagates in a rectangle or semi-circular arch space were described and the information of location and direction at arbitrary point on the paths was explored.Based on time series extracted from points on the paths with equal length,we calculated the largest Lyapunov exponents(LLEs)of ray systems in two spaces using Wolf algorithm.The results show that: the ray in the rectangle geometry moves regularly with LLE approaching to 0,whereas the ray in the concave space performs partly chaotic characteristics with a positive LLE.By an application of ray chaos to building acoustics,the sound field uniformity should be better in the concave room.Uniformity indicated by the differences of the sound pressure level(SPL)at different positions was simulated using the acoustic software ODEON.The results show that sound field uniformity in the concave room is better than that in the rectangle room.Moreover,we theoretically established a method of mapping ray movement in three-dimensional enclosures and used a ray-tracing algorithm to describe the paths along which the ray propagates in spaces with a slope or Sinai geometry.Time series points extracted from the paths were used to calculate the largest local Lyapunov exponents(LLLEs).We investigated the LLLE distributions for ray systems in the two spaces.The distributions contained considerable information on the ray system dynamics;this information can be used to study the evolution of ergodic properties.A comparison of the LLLEs of the ray systems in the two spaces showed that the Sinai geometry produced a diffusive characteristic,whereas the slope geometry produced flutter echo.By an application of the method to building acoustics,the acoustic fields in different rooms were described.A diffuse acoustic performance was indicated by the uniformity of the sound pressure level(SPL)using the acoustic software ODEON.The results show that LLLEs have potential for use in acoustic performance description.In the experiment,Sinai and three-dimensional rectangular rooms were selected.The SPLs at 10 receiving points in two rooms further showed that the sound field uniformity in the Sinai room was better than that in the three-dimensional rectangular room.