The consider a simple model arising in the control of noise. We assume that the two-dimensional cavity Omega = (0, 1) x (0, 1) is occupied by an elastic, inviscid, compressible fluid. The potential phi of the velocity field satisfies the linear wave equation, The boundary of Omega is divided into two parts, Gamma(0) and Gamma(1). The first one, Gamma(0), is flexible and occupied by a vibrating string that obeys the one-dimensional wave equation. On Gamma(0) the continuity of the normal velocities of the fluid and the string is imposed. The subset Gamma(1) of the boundary is assumed to be rigid, and therefore, the normal velocity of the fluid vanishes. This constitutes a conservative system of two coupled nave equations in dimensions two and one, respectively. The control (an elastic force or an exterior source of noise) is assumed to act on the flexible part of the boundary. We are interested on the controllability problem : given a large enough control time, what are the initial conditions we can drive to the equilibrium bu means of, say, L-2-controls? By using Fourier series the problem is decomposed into an infinite number of one-dimensional control problems that we serve by classical methods that combine the Hilbert uniqueness method, multiplier techniques, and Ingham-type inequalities. Putting these one-dimensional results together, we give a precise characterization of the space of controllable data in terms of Fourier series.