Wow, that is an excellent application note and is very helpful. I may try both the 555 and TI driving ideas since they are both very similar and require minimal parts. My transducers are small, so I imagine it won't take an incredible amount to drive them.
The piezo ultrasonic transducers are behaving like a ceramic capacitor. At resonance, they become resistive in their equivalent circuit. As their load is only air, they transmit some power by ultrasound with not much of efficiency. I used the 24 and40 kHz devices to transmit simple commands over a couple of meters, with a 555 as a generator, and some IRF power FET as the power amplifier. The FET was powered by 12 VDC through a transformer on a ferrite core, and at resonance the voltage peaked over 100 V across the transducer.
As I wrote, to check the function of my transmitter, I used another transducer connected to an oscilloscope. At resonance (and quite sharp, like < 1%) the system response was clear and the waveform on the scope was sinusoidal. On the transmitting transducer, the waveform was rather pulse-like. I think it does not matter if one drives the transducer by a rectangular or sinusoidal voltage.
I did not make a high-power "cleaning" type devices but I repaired one. The power driver is typically a switching-type power amplifier, with a transformer. The water-loaded transducers do not need an exact frequency ; the resonance is wider ~5%, and efficiency, too. A typical electrical drive power is 50-100 W and liquid cooling removes the heat. It is not recommended to run them dry.
When power FETs are used with not exactly resistive loads, they need the overvoltage protection. Some devices have built-in diodes. To be sure, connect one more diode to swallow the reactive overvoltage, and select rather high-voltage device to prevent burnout. Also, be sure you do not touch the live line at operation, 100 V peak and more hurts quite well. Also, do not expose your ears to the high-power ultrasound. You cannot heAr it but it can hurt your inner ear.