The article deals with the study of the nonlinear coefficient inverse problem for the wave equation in a 3D bounded domain with a boundary condition of the third kind. Given a family of equation solutions on a closed surface inside the domain, it is required to recover the coefficient at the second time derivative which determines sound velocity profile in the inhomogeneous medium. The inverse problem under examination is reduced to the linear integral equation of the first kind. The authors establish the unique solvability of the obtained equation and provide results of the numerical experiment.