Sound waves in a wave noise

We examine by analytical and numerical means sound waves which propagate in a space- and time-dependent random mass density field in the form of dispersionless wave noise of its spectrum E(kappa,omega) ~ E(kappa) delta (omega-crk), where cr is a random speed. Numerical simulations are in agreement with the analytical theory which shows that at cr=omega/k resonance occurs and the cyclic frequency omega tends to infinity. For values of cr which are close to the resonance point, the sound waves are slowed down and attenuated (accelerated and amplified) for cr < omega/k (cr > omega/k).