  We prove existence and uniqueness of $L^2$ solutions to the inhomogeneous
wave equation on $\mathbb{R}^{n-1}\times\mathbb{R}$ under the assumption that
the inhomogeneous data lies in $L^p(\mathbb{R}^n)$ for $p=2n/(n+4)$. We also
require the Fourier transform of the inhomogeneous data to vanish on an
infinite cone where the solution could become singular. Subsequently, we show
sharpness of the exponent $p$. This extends work of Michael Goldberg, in which
similar Fourier-analytic techniques were used to study the inhomogeneous
Helmholtz equation.
