We consider in this paper the existence and numerical estimation of an optimal boundary control for the linear wave equation. The problem is modified into one consisting of the minimization of a linear functional over a set of Radon measures; the optimal measure is then approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this problem is used to construct a piecewise-constant control. Some numerical examples are considered to illustrate the procedure.