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In this paper, the mechanism of sound generation by flow over twocavities in two dimensions is studied by examining the evolution of vorticity,, pressure level, spectra and directivity of the generated sound. The study shows that the sound pressure level for two cavities is higher than that for a single cavity. When the distance between the two cavities is large, the interaction between vortices caused by cavities is weak enough to be negligible, so that the results from the acoustic analogy approach coincide with those from the superposition principle. When the distance between the two cavities is relatively small, however, the interaction between vortices becomes stronger and the results from acoustic analogy approach are then larger than those from the superposition principle. Regarding the nonlinear interaction of sound waves in the far field, high harmonic waves will occur when the dimensions of the two cavities are equal, while the sum and difference frequency waves besides the high harmonic waves will appear when the dimensions of the two cavities are different.