Let v(x,t), \(x\in {\mathbb{R}}\), denote the displacement of an infinitely long, idealized string performing damped vibrations caused by an initial spatial (one-parameter) white noise. Upper and lower bounds for the distribution of \(\max_ sv(x,s)\) and \(\max_ xv(x,t)\) are obtained. The case where the deterministic second order equation is additively perturbed by a space-time (two-parameter) white noise is also analyzed. Finally, a section is devoted to the case of a semi-infinite string performing damped vibrations. v(x,t) is represented as the mild solution to the corresponding linear second order equation using the Green’s function.