Consider the wave equation with constant or variable coefficients in $\R^3$.
The initial datum is a random function with a finite mean density of energy
that also satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition.
The random function converges to different space-homogeneous processes as
$x_3\to\pm\infty$, with the distributions $\mu_\pm$. We study the distribution
$\mu_t$ of the random solution at a time $t\in\R$. The main result is the
convergence of $\mu_t$ to a Gaussian translation-invariant measure as
$t\to\infty$ that means central limit theorem for the wave equation. The proof
is based on the Bernstein `room-corridor' argument. The application to the case
of the Gibbs measures $\mu_\pm=g_\pm$ with two different temperatures $T_{\pm}$
is given. Limiting mean energy current density formally is $-\infty\cdot
(0,0,T_+ -T_-)$ for the Gibbs measures, and it is finite and equals to
$-C(0,0,T_+ -T_-)$ with $C>0$ for the convolution with a nontrivial test
function.