A stochastic model for acoustic attenuation

Propagation of waves in gases or liquids has been observed for a long time in homogeneous or non-homogeneous media. In acoustics, attenuation is a significant problem which is studied mainly through the 'equations of change' of fluid mechanics. These equations are based only on the macroscopic characteristics of the medium. Microscopic variations, related to other phenomena like Brownian motion or critical opalescence, are not taken into account. This paper provides a random one-ray model. This model explains the proportionality between the standard attenuation and the product between length and frequency squared in a logarithmic scale. The wave is shown to be necessarily associated with noise, even if this noise cannot be observed by devices. Furthermore, the 'coefficient of variation' defined in turbulent environments can be explained as a random version of the usual coefficient of attenuation.