An ultrasonic vibrator has a single natural frequency for radiating ultrasonic energy into a cleaning solution to clean and deburr workpieces that are immersed in the cleaning solution. A plurality of oscillating signals having respective different frequencies which are integral multiples of the natural frequency of the ultrasonic vibrator are generated, and successively outputted for respective periods of time thereby to generate a composite signal which is composed of a time series of the oscillating signals. The composite signal is applied as a drive signal to the ultrasonic oscillator to oscillate the ultrasonic vibrator. The oscillating signals may be outputted successively for said respective periods of time or intermittently with quiescent periods inserted therebetween.