Frequency and amplitude alterations of sound modes in a space-dependent random mass density field

We investigate the effect of a space-dependent random mass density field on small amplitude acoustic modes that are settled in a semi-infinite medium of a temperature growing linearly with depth. Using a perturbation method, the dispersion relation is derived in the form of Hill’s determinant. Numerical solutions of this equation lead to the following conclusions: (a) a weak random field (with σeff = 0.05) essentially affects long waves which experience attenuation and a frequency reduction; (b) for a stronger random field (with σeff = 0.1), high-order sound modes behave as sound waves as they are attenuated and their frequencies are increased; (c) for a sufficiently strong random field (with σeff = 0.2), mode coupling occurs, as a result of which the dispersive curves cross each other, the sound modes loose their identities, and some modes are amplified. Here σeff denotes the effective strength of a random field.