  Under consideration is the damped semilinear wave equation \[
u_{tt}+u_t-\Delta u + u + f(u)=0 \] on a bounded domain $\Omega$ in
$\mathbb{R}^3$ with a perturbation parameter $\varepsilon>0$ occurring in an
acoustic boundary condition, limiting ($\varepsilon=0$) to a Robin boundary
condition. With minimal assumptions on the nonlinear term $f$, the existence
and uniqueness of global weak solutions is shown for each
$\varepsilon\in[0,1]$. Also, the existence of a family of global attractors is
shown to exist. After proving a general result concerning the
upper-semicontinuity of a one-parameter family of sets, the result is applied
to the family of global attractors. Because of the complicated boundary
conditions for the perturbed problem, fractional powers of the Laplacian are
not well-defined; moreover, because of the restrictive growth assumptions on
$f$, the family of global attractors is obtained from the asymptotic
compactness method developed by J. Ball for generalized semiflows. With more
relaxed assumptions on the nonlinear term $f$, we are able to show the global
attractors possess optimal regularity and prove the existence of an exponential
attractor, for each $\varepsilon\in[0,1].$ This result insures that the
corresponding global attractor inherits finite (fractal) dimension, however,
the dimension is {\em{not}} necessarily uniform in $\varepsilon$.
