The Nature of Sound Fluctuation in Continuous, Statistically Isotropic Media

Abstract

An analytic procedure is developed for obtaining the Lagrangian measure function B(χ, ξ|s) from its characteristic function φ(k, ξ|s) for stochastic-Fermat media. This permits the calculation of the (Eulerian) ensemble average of the pressure wave, 〈p(χ)〉, as well as 〈|p|2〉, via a central limit theorem for stochastic Lagrangian functionals. This results in a coefficient of intensity variation V that evinces a frequency-dependent phase-dominance region and a frequency-independent amplitude-dominance region. The methods employed in this study are new to the problem of sound propagation through continuous stochastic media and avoid three common difficulties: (1) range limitations due to cumulative phase effects; (2) discrete scattering associations; and (3) restriction to an Eulerian path.