Modelling of sonic textures by homogenization

Abstract

A periodic network is studied with homogenization methods when the nodes are occupied according to Xenakis's model of probabilistic cloud. As the network period shrinks to the null size, the equivalent texture acquires sound properties that depend on the ratio of the high density locations size over the period of their distribution. Three cases are considered according to some critical value of this ratio. The asymptotic pressure characteristic of the limit problem is determined under the assumption that some fundamental frequency is finite and positive.

Keywords:

• dynamics
• harmonics
• intervals
• pitch
• space
• texture

Mathematical Subject Classification 2000 :

• 35B27
• 35K57
• 76R50