In this paper, we study the following stochastic wave equation on the real line: \(\partial _t^2 u_{\alpha }=\partial _x^2 u_{\alpha }+b\left( u_\alpha \right) +\sigma \left( u_\alpha \right) \eta _{\alpha }\) . The noise \(\eta _\alpha \) is white in time and colored in space with a covariance structure \(\mathbb {E}[\eta _\alpha (t,x)\eta _\alpha (s,y)]=\delta (t-s)f_\alpha (x-y)\) where \(f_\alpha \) is continuous with respect to \(\alpha \) in Fourier mode, see Assumption 1.2. We prove the continuity of the probability measure induced by the solution \(u_\alpha \) , in terms of \(\alpha \) , with respect to the convergence in law in the topology of continuous functions with uniform metric on compact sets. We also give several examples of \(f_{\alpha }\) to which our theorem applies.
