I want to use ultrasonic (20 kHz to 100 kHz) transducers to couple ultrasound into pipes for cleaning purposes. You can easily buy those transducers with driving circuits on Aliexpress but I want to do experiments on the coupling link and would like to measure how much power is transmitted into the water. Using microphones inside the pipe is very complicated, so I thought it might be smarter to distinguish transmitted power from the transducer site. I thought maybe I would be able to use a VNA like RF-engineers use to estimate the transmitted power.
Additionally, I wonder how I would be able to distinguish heat produced in the transducer and transmitted power into the water.
Then my third question would be what the right model for those transducers is. At first I was thinking about them as a mechanical oscillator. The piezo acting as a spring and the back and front pieces as masses, but now I think the better approach is to think of them as standing waves inside the transducer. What is the correct argument against the spring-mass model?