Yes, definitely you can drive ultrasonic transducer by continuous wave or tone burst or a sharp pulse. It depends on the type of transducer and it's resonant frequency. If you can share more details probably I can suggest more.
Sir Actually I want to make sonicator bath in laboratory. So I was planning to by transducer and fix it to steel pot. And drive that transducer using function generator.
Actually sonicator transducers generally operate at 40kHz or see the datasheet. Only the point is that these transducers consume higher power (generally few 10s of Watts). The normal function generator will not be able to pump the amount of power needed. You need power amplifier to drive the transducer. I suggest the low cost commercial drivers available. The similar products you can see on the following link.