  Under consideration is the damped semilinear wave equation \[
u_{tt}+u_t-\Delta u+u+f(u)=0 \] in a bounded domain $\Omega$ in $\mathbb{R}^3$
subject to an acoustic boundary condition with a singular perturbation, which
we term "massless acoustic perturbation," \[ \ep\delta_{tt}+\delta_t+\delta =
-u_t\quad\text{for}\quad \ep\in[0,1]. \] By adapting earlier work by S.
Frigeri, we prove the existence of a family of global attractors for each
$\ep\in[0,1]$. We also establish the optimal regularity for the global
attractors, as well as the existence of an exponential attractor, for each
$\ep\in[0,1].$ The later result insures the global attractors possess finite
(fractal) dimension, however, we cannot yet guarantee that this dimension is
independent of the perturbation parameter $\ep.$ The family of global
attractors are upper-semicontinuous with respect to the perturbation parameter
$\ep$, a result which follows by an application of a new abstract result also
contained in this article. Finally, we show that it is possible to obtain the
global attractors using weaker assumptions on the nonlinear term $f$, however,
in that case, the optimal regularity, the finite dimensionality, and the
upper-semicontinuity of the global attractors does not necessarily hold.
