We think the primary issue was using a transducer that was vastly underpowered compared to commercial (and expensive) ultrasonic cutters, but we suspect the horn he machined was probably not ...

[Lindsay] has a wonderful writeup about a new toy in the shop, an ultrasonic transducer. The 28kHz, 70W bolt-clamped Langevin transducer by itself is not much use, you need a power supply, a horn ...