Assuming roughly planar waves come off the ultrasonic transducer head, it should be possible to focus them with a lens. After turning acrylic on a lathe didn’t work, I ordered a 3D printed part and tried this.
The plastic normally seemed decently durable, but in several seconds the edge of the lens started curling up and ended up looking like the above. It was pretty warm to the touch and the browning seems to be due to the heat.
So why did this happen? To be honest, I have no idea but a first thing to test would be to thicken the edge. That angle may also be at the Brewster’s angle, which is the angle which gives total reflection (like glass at small angles is reflective). Unlike Snell’s law, Brewster’s angle is not perfectly analagous between light and sound. https://www.sciencedirect.com/science/article/abs/pii/0041624X95001018 The material might also just be too absorptive of the vibrational energy.
I’m still working on measuring the speed of sound and damping coefficient for sound waves in the rod.