<p>The studies on the hydroacoustic waves in an inviscid compressible fluid are of great interest among the scientific community due to its physical significance and engineering applications. A deep survey, as shown in this article, indicates that there are different governing equations for the waves and the flows under several mathematical approximations. Revealing the mathematical origins and the applicable conditions for these governing equations is the aim of the present work. In the framework of the potential theory for an inviscid compressible fluid with irrotational flows, we re-derive the nonlinear governing equations for a general case with the nonnegligible convective effects. Then a couple of special examples are demonstrated and some relevant researches are reviewed. In particular, we find the meaning of a highly concerned term <i>g</i>(<i>∂Φ/∂z</i>) is due to the combined effects of the vertical gravitational acceleration and the flow convection, where <i>g</i> and <i>Φ</i> are respectively the gravitational acceleration and the velocity potential. Finally the well-known wave equation is obtained for the propagation of small disturbances in an initially stationary homogeneous fluid, in a mathematically and physically rigorous way, without the frequently-used assumption that the hydrostatic pressure is constant, putting emphasis on Batchelor’s viewpoint (1967) that, when there is a free surface or interface for the fluid, the gradient of the hydrodynamic pressure should be employed for the equation of momentum without the gravitational force.</p>