Sound absorption by Menger sponge fractal.

For the purpose of investigation on acoustic properties of fractals, the sound absorption coefficients are experimentally measured by using the Menger sponge which is one of typical three-dimensional fractals. From the two-microphone measurement, the frequency range of effectively absorbing sound waves is shown to broaden with degree of fractality, which comes from the fractal property of the homothetic character. It is shown that experimental features are qualitatively explained by an electrical equivalent circuit model for the Menger sponge.

Application of Hamiltonian of ray motion to room acoustics.

Based on a standard Hamiltonian of acoustic ray, it is shown that a ray motion in a finite region can be treated as a particle motion inside a potential well. The boundary reflections of ray can be described by introducing a so-called confining potential to confine a ray motion in a closed domain. It is shown that the square well potential model for the ray motion can reproduce the reverberation time in a two-dimensional room with irregular walls which is consistent with the Norris-Eyring law. It is also shown that the sound reverberation relates the ray chaos of the billiards in polygons with smooth convex walls.