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This work is devoted to investigating a compressible fluid system with lowstratification, which is driven by fast acoustic waves and internal waves. Theapproximation using a soundproof model is justified. More precisely, thesoundproof model captures the dynamics of both the non-oscillating mean flowsand the oscillating internal waves, while filters out the fast acoustic waves,of the compressible system with or without initial acoustic waves. Moreover,the fast-slow oscillation structure is investigated.

The soundproof model of an acoustic--internal waves system with low stratification