  In this article, we study the asymptotic behavior of the spatial integral of
the solution to the hyperbolic Anderson model in dimension $d\leq 2$, as the
domain of the integral gets large (for fixed time $t$). This equation is driven
by a spatially homogeneous Gaussian noise, whose covariance function is either
integrable, or is given by the Riesz kernel. The novelty is that the noise does
not depend on time, which means that It\^o's martingale theory for stochastic
integration cannot be used. Using a combination of Malliavin calculus with
Stein's method, we show that with proper normalization and centering, the
spatial integral of the solution converges to a standard normal distribution,
by estimating the speed of this convergence in the total variation distance. We
also prove the corresponding functional limit theorem for the spatial integral
process.
