Numerical Simulations of Random Sound Waves

We perform one-dimensional numerical simulations of both driven and impulsively generated sound waves propagating through a medium whose mass density admits time-independent, random fluctuations. While the amplitude of both types of waves is always attenuated, driven sound waves can be either retarded or speeded-up depending on their wavenumber, amplitude and on the strength of random field. The speed of a pulse propagating in the random medium is also altered, in agreement with the findings for the driven waves. The concomitant action of nonlinearity and randomness results in wave speeding for wavenumbers which are of the order of the size of an average random density fluctuation, whereas it gives retardation for larger wavenumbers.