  We study the vanishing Mach number limit for the stochastic Navier-Stokes
equations with $\gamma$-type pressure laws, with focus on the one-dimensional
case. We prove that, if the stochastic term vanishes with respect to the Mach
number sufficiently fast, the deviation from the incompressible state of the
solutions (for $\gamma \geq 1$) and the invariant measures (for $\gamma = 1$)
is governed by a linear stochastic acoustic system in the limit. In particular,
the critically sufficient decay rate for the stochastic term is slower than the
corresponding results with deterministic external forcing due to the martingale
structure of the noise term, and the blow-up of the noise term for the
fluctuation system can be allowed.
