The paper presents formulas for the statistical moments of a plane sound wave propagating in moving random media (the turbulent atmosphere and ocean, turbulent flows of gases and fluids, etc.) with arbitrary spectra of temperature and medium velocity fluctuations. These statistical moments, which are most often of interest, are the following: the variances of log-amplitude and phase fluctuations, the correlation functions of log-amplitude and phase fluctuations, the mean sound field, the coherence function of a sound field, and the sound scattering cross section per unit volume. These statistical moments are calculated for Gaussian spectra of temperature and medium velocity fluctuations. It is shown that the contributions to the statistical moments due to sound scattering by medium velocity fluctuations may dramatically differ from those due to sound scattering by temperature fluctuations.