An ultrasonic transducer (1) is excited by the output signal of a voltage-controlled oscillator (4). The latter is controlled (6, 7) with a delta generator (5) in such a way that its frequency is periodically swept in a range enclosing the series resonance of the ultrasonic transducer. A measured variable (I, V) corresponding to the damping of the ultrasonic transducer is formed and compared with a maximum admissible damping. If the detected damping is smaller than the maximum admissible damping, the oscillator (4) is additionally controlled as a function of the measured variable. This is preferably a function of the excitation current (I) of the ultrasonic transducer. Preferably, an instantaneous value (24) and a delayed value (8) are formed therefrom and their difference compared (9) with a threshold value: if this difference is equal to the threshold value, the sweeping device (7, 5) is reversed. The power at the ultrasonic transducer can then be controlled by varying the operating voltage (U) of the output stage (2) connected upstream of the ultrasonic transducer. … The method can be used for atomising a liquid by means of an ultrasonic transducer provided with an atomising plate. … …