  The Hausdorff dimension of an exceptional set of periods for which
convergence of a formal solution to an inhomogeneous wave equation in n spatial
and one temporal dimension is problematic, is determined along with conditions
which the periods must satisfy to ensure the solvability of the inhomogeneous
wave equation by a smooth periodic function. To derive this information, a
complete metric theory for a related fully nonlinear Diophantine approximation
problem involving perfect squares is established.
