On the random wave equation within the mean square context

<p style='text-indent:20px;'>This paper deals with the random wave equation on a bounded domain Dirichlet boundary conditions. Randomness arises from velocity wave, which is positive variable, and two initial conditions, are regular stochastic processes. The aleatory nature of inputs mainly justified data errors when modeling motion vibrating string. Uncertainty propagated these to output, so that solution becomes smooth field. We focus mean square contextualization problem. Existence uniqueness exact series solution, based upon classical method separation variables, rigorously established. Exact for variance process obtained, converge at polynomial rate. Some numerical examples illustrate facts.</p>