# Estimate transmitted ultrasonic power

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?

• Is this a metal pipe. is the exciter shaped for external agitation of the pipe? Is it 40kHz or lower for greater cavitation energy? Commented Aug 13, 2021 at 21:01

To measure acoustic power you need to find the source level (SL) and directivity index (DI). The following is needed:

• A calibrated hydrophone. These tend to be expensive (> USD 1000). You may be able to source hydrophones from surplus sonobuoys. These are calibrated with the sensitivity stamped on the hydrophone. You could find an uncalibrated hydrophone and use reciprocity calibration to calibrate it, but this is a tedious procedure.
• A body of water to perform the tests (swimming pool, jacuzzi, lake, ...), large enough so you're out of the near field.
• Signal source capable of outputting a periodic burst signal at the frequency of interest.
• An oscilloscope, preferably a digital scope since the rep rate will be pretty slow (perhaps 10Hz).
• Rigging to hold the projector(your transducer) under test & the reference hydrophone steady.

Acoustic power is a difficult thing to calculate from the source level (SL) you'll be measuring since you need to know the directivity index (DI) of the projector. A small error in DI will cause a large error in the power calculation. If your projector is a disc, you can use an equation to roughly estimate the DI. To get an accurate DI you need to do a full 2D beam pattern which requires a full lab as found at NPL and some universities.

Of course, all the above is meaningless since you'll be in the near field which is hard to define signal strengths. Empirical measurements are ultimately what you will be doing.

As for how a transducer works, a dampened mass-spring system is normally used for the analogy for the ceramic. However, waves are present in the transducer housing and how they interact with the backing material (reflective or absorptive) and the impedance matching with the water need to be taken into consideration.

If you want to proceed further on the power issue and have the test equipment to do so, say so and I can provide additional equations for estimating acoustic power.

• i am willing to do the work, but dont you think i can do the measurement from the transducer side with a VNA or so?
– x3oo
Commented Aug 13, 2021 at 19:56
• VNA is useful if it has an impedance measuring capability since you will need to know the complex admittance of your transducer, however, this measurement is better suited for and impedance analyzer like the HP4194 since high-Z may be present. For network analysis, it may not handle the output to input time delay (1 to 4ms) very well, plus, you will be dealing with pulses (small tanks have reflections), not continuous signals unless you have a very large tank (perhaps >20m). A good DSO, one that has decimation to increase bit depth, is better suited for sensitivity measurements.
– qrk
Commented Aug 13, 2021 at 20:46