A study of wave radiation by a piston bottom displacement, in a compressible ocean of constant depth, is carried out within the framework of a two-dimensional linear theory. Simple analytic expressions for the flow field, at a large distance from the disturbance, are derived. A realistic numerical example indicates that the Acoustic-Gravity waves, which significantly precede the tsunami, are expected to leave a significant signature on bottom-pressure records that should be considered for early detection of tsunamis.