Phase and amplitude fluctuations in the propagation of acoustic waves in lossless inhomogeneous continua with velocity, density and bulk modulus variations

Abstract

Discussions of the phase and amplitude fluctuations of waves travelling through inhomogeneous media have previously considered only fluctuations caused by the variation of sound velocity in the medium, density variations being ignored since in water and air they can be shown to be small. In biological tissues this assumption cannot be made, and this paper derives the fluctuation dependence on velocity and density variations of characteristic dimension large compared to the wavelength. Previous discussions have shown a more appropriate formulation to be that of the fluctuation dependence on bulk modulus and density variations and this analysis is presented for the first time. The form of the solutions is shown to be simplified for extreme values of the wave parameter, but formulae for comparison with experiment require the specification of the analytical form of the correlation coefficients of the parameter variations. The fluctuations for correlation coefficients of the form exp (− r 2/ a 2) are evaluated both for the general case, and for extreme values of the wave parameter. It is found that the density variations contribute to the fluctuations only insofar as they are cross-correlated with the velocity fluctuations (for velocity and density variations); while the amplitude fluctuations, for small values of the wave parameter and the specific form of correlation coefficients used, are independent of frequency.