  This work is devoted to investigating a compressible fluid system with low
stratification, which is driven by fast acoustic waves and internal waves. The
approximation using a soundproof model is justified. More precisely, the
soundproof model captures the dynamics of both the non-oscillating mean flows
and 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.
