  We consider the problem of the numerical approximation of the linear
controllability of waves. All our experiments are done in a bounded domain
\Omega of the plane, with Dirichlet boundary conditions and internal control.
We use a Galerkin approximation of the optimal control operator of the
continuous model, based on the spectral theory of the Laplace operator in
\Omega. This allows us to obtain surprisingly good illustrations of the main
theoretical results available on the controllability of waves, and to formulate
some questions for the future analysis of optimal control theory of waves.
