The author obtains an observability estimate of the type
where denotes the weak solution of the problem in , on , in . The potential is assumed essentially bounded in and denotes a subdomain of the bounded domain in with boundary . The main novelty of the paper is the explicit estimate of the constant with respect to : in fact, it is proved that as . As usual, this type of estimates can be applied to get the exact internal controllability in at (sufficiently large) time of the semilinear wave equation in , where with , by choosing the control in .