High-frequency plasma discharges are often sustained by collisionless heating of electrons; the nature of these mechanisms is a central problem in the theory of such discharges. In capacitive discharges, collisionless heating occurs near boundaries, and is usually attributed to inelastic collisions of electrons with oscillating plasma sheaths, regarded as moving rigid barriers. We show that, when current conservation is required, such heating necessarily vanishes, and we conclude that this model of the heating process is not correct. We develop an alternative view that associates the heating with acoustic disturbances in the electron fluid. An analytic model, based on moments of the Vlasov equation, gives results in good agreement with particle-in-cell simulations. In terms of individual particle dynamics, this acoustic heating may be interpreted as a transit-time effect.