  In this paper we study asymptotic properties of the maximum likelihood
estimator (MLE) for the speed of a stochastic wave equation. We follow a
well-known spectral approach to write the solution as a Fourier series, then we
project the solution to a $N$-finite dimensional space and find the estimator
as a function of the time and $N$. We then show consistency of the MLE using
classical stochastic analysis. Afterward we prove the asymptotic normality
using the Malliavin-Stein method. We also study asymptotic properties of a
discretized version of the MLE for the parameter. We provide this asymptotic
analysis of the proposed estimator as the number of Fourier modes, $N$, used in
the estimation and the observation time go to infinity. Finally, we illustrate
the theoretical results with some numerical experiments.
