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Ultrasonic Piezo - How to get rid of audible buzz?

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Yes, on resonance with other parts: if you use a function generator to generate the 40 kHz try adjust the output up or down to see if the buzzing disappears. Something in the frame could be resonating with a lower frequency harmonic, even if its a sine wave outputted, the actual output of the piezo could be distorted.

The buzz could be caused by an induced resonance of the support on which the piezo is mounted.
 
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Yes, on resonance with other parts: if you use a function generator to generate the 40 kHz try adjust the output up or down to see if the buzzing disappears. Something in the frame could be resonating with a lower frequency harmonic, even if its a sine wave outputted, the actual output of the piezo could be distorted.

If I adjust the frequency the voltage across the piezo changes and so does the ticking sound. The mounting is a soft silicone rubber which can't really vibrate, but I have been thinking about other possibly resonances, for example from the solder blob and leads, although I don't know how that would work. I'm also currently making up a few new piezos with a different epoxy resin and steel parts to see what effect that might have.
 
Play with it then; change the waveform to square, any change? if not alter the duty cycle; Experiment to find the sweet spot, you may find a compromise without having to use different materials in your build. Because the crystal deforms and flexes like a speaker it can induce a voltage that will feedback into the FG and also generate its own crackle as it snaps. You should beware of this and bleed this voltage out to avoid unwanted noise. A series resistor may help see pdf:

https://www.electro-tech-online.com/custompdfs/2011/09/p15e.pdf
 
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