  We use some new nonlinear estimates found in \cite {LM} to improve the
results of \cite{GL} that establish the acoustic limit for DiPerna-Lions
solutions of Boltzmann equation in three ways. First, we enlarge the class of
collision kernels treated to that found in \cite{LM}, thereby treating all
classical collision kernels to which the DiPerna-Lions theory applies. Second,
we improve the scaling of the kinetic density fluctuations with Knudsen number
from $O(\epsilon^m)$ for some $m>\frac12$ to $O(\epsilon^\frac12)$. Third, we
extend the results from periodic domains to bounded domains with impermeable
boundaries, deriving the boundary condition for the acoustic system.
