Abstract A bounded inhomogeneity D is immersed in an acoustic medium; the speed of sound is a function of position in D, and is constant outside. A time-harmonic source is placed at a point y and the pressure at a point x is measured. Given such measurements at all for all x ∈ P, for all y ∈ P where P is a plane that does not intersect D, can the speed of sound (in the unknown region D) be recovered? This is a velocity-inversion problem. The three-dimensional problem has been solved analytically by Ramm (Phys. Lett. 99A, 258-260 (1983)). In the present paper, analogous one-dimensional and two-dimensional problems are solved, as well as the problem where the plane P is the interface between two different acoustic media.