The waveform isn't produced by the transducer, whether it be square, sine, or triangle.
Electrical waveforms are generally generated by circuits called "function generators", the simplest being made with the 555 chip (which produces square waves at a maximum frequency of around .16 Mhz). The function generator that these scientists used was a bit more expensive than a 15 cent 555 chip, but it had far more options than were needed. You can make a 1 Mhz function generator for cheap (see one of my previous posts for a link).
The waveforms are likely fed to a high-frequency power transistor as to prevent damage to the function generator from too much current draw. However, since the one they used was one of the more fancy models, it may have included higher power levels.
Anyways, the waveform then goes to the transducer, where it is transduced into mechanical energy. Square waves are used with piezoelectric elements because they function better under on-off waveforms as opposed to those with varying levels of amplitude (which is why you don't use them for computer speakers or headphones).
As far as the transducer goes, as long as it can handle the required frequency, it doesn't have any effect on the waveform that is fed to it.