An inverse problem for the wave equation outside an obstacle with a dissipative boundary condition is considered. The observed data are given by a single solution of the wave equation generated by an initial data supported on an open ball. An explicit analytical formula for the computation of the coefficient at a point on the surface of the obstacle, which is nearest to the center of the support of the initial data, is given. Copyright (C) 2016 JohnWiley & Sons, Ltd.