  In this paper, we consider three-dimensional nonlinear stochastic wave
equations driven by the Gaussian noise which is white in time and has some
spatial correlations. Using the Malliavin-Stein's method, we prove the Gaussian
fluctuation for the spatial average of the solution under the Wasserstein
distance in the cases where the spatial correlation is given by an integrable
function and by the Riesz kernel. In both cases we also establish functional
central limit theorems.
