  We study the one-dimensional stochastic wave equation driven by a Gaussian
multiplicative noise which is white in time and has the covariance of a
fractional Brownian motion with Hurst parameter $H\in [1/2,1)$ in the spatial
variable. We show that the normalized spacial average of the solution over
$[-R,R]$ converges in total variation distance to a normal distribution, as $R$
tends to infinity. We also provide a functional central limit theorem.
