The equations of resistive magnetohydrodynamics taking into account the Hall effect are solved analytically for the case of a planar plasma flow across the magnetic field. Waves of purely acoustic nature are revealed that propagate in the plasma medium on the background of a steady magnetically accelerated plasma flow of a rather arbitrary form. The magnetic field manifests itself in this process only in that it produces an effective gravity force, the ‘gravitational’ acceleration being proportional to ωeτe. Like acoustic–gravity waves in the atmosphere, such quasi- acoustic–gravity (QAG) waves in a plasma can increase greatly in amplitude as they propagate ‘upwards’, i.e., in this case, counter to the direction of the electric field. In a plasma channel (where the plasma flows between the electrodes), a system of standing QAG waves arises, which has a stationary component. These waves are responsible for a number of distinctive features in the behaviour of Hall plasma flows, in particular for very large gradients and unexpected small-scale fluctuations of physical quantities near the anode, revealed earlier by numerical simulation. In the cases where the plasma-flow parameters provide a high intensity of these fluctuations, the flow appears to be unstable. In another range of parameter values, the QAG waves are strongly coupled with the electric currents that they induce in the electrodes, their amplitudes increase with time, and, again, the flow cannot be steady. The existence of a rather general dimensionless similarity criterion for resistive Hall plasma planar flows is also shown. This criterion can be found directly from the structure of the equations without any restrictions on the plasma parameters or on the form of the flow.