In this paper the problem of parametric sound generation in an acoustic resonator filled with a fluid is considered, taking explicitly into account the influence of the nonlinearly generated second harmonic. A simple model is presented, and its stationary solutions were obtained. The main feature of these solutions is the appearance of bistable states of the fundamental field resulting from the coupling to the second harmonic. An experimental setup was designed to check the predictions of the theory. The results are consistent with the predicted values for the mode amplitudes and parametric thresholds. At higher driving values a self-modulation of the amplitudes is observed. This phenomenon is identified with a secondary instability previously reported in the frame of the theoretical model.