I have ZERO familiarity as I never wore a watch until I got my first Apple watch a few years ago.

   I have never played with these devices, but out of curiosity, I did a quick Google around. So just a few random notes from what I saw ... sorry it is not an answer, but I hoped something might trigger a thoght.

I tried the EDN ASIA reference, but there were no figures, excepting a generic circuit with no electronic resonant components. So I couldn't read the full story, an dit didn't help much.

-----------

As Ron @zander says, some devices are packaged with electronics, so it is only necessary to supply an appropriate dc voltage for the electronics, say 3-5V to enable it to be directly driven by an Arduino.

Others, are the 'raw' device. Typical drive voltages appeared to go up to about 200 V (peak), although lower voltages (say 20V) can be sufficient in appropriate circumstances. That voltage needs to oscillate at the frequency of sound to be emitted.

------------

The acoustic resonant frequency of the transducer appears to be a complicated quantity, not just a single fixed value. Sorry, I haven't followed it through properly, but I saw suggestions that it might be necessary to find it experimentally. Perhaps this has some connection with your observation of different frequencies when you try to calculate the electronic resonant frequency?

-------------

I suspect a significant part of maximising the acoustic output, especially when the power source is limited, is determined by the mechanical design surrounding the transducer.

The frequencies you mention are in the range 40 kHz to 80kHz, which are inaudible to humans .. These values suggest reference to an ultrasonic transducer .. not an alarm for a clock or watch, which presumably would need to be nearer 1kHz.

Best wishes, Dave

-fish

There is a section in here on the alarms!  It shows the following circuit:

You can see the alarm circuit on the right.  I guess you feed the PWM signal from the controller (I would be using an esp32) to the base of the NPN transistor.  Then you have a resonator with the piezo and inductor in parallel.  I was able to find a more detailed explanation here:https://www.ednasia.com/increase-piezoelectric-transducer-acoustic-output-with-a-simple-circuit/?rd=1

Note the author in the link above tries to pass this off as a "new" idea.  Anyway, I started to read this and immediately had the following question: 

The author states, "The electrical resonance frequency need not be the same as that of the acoustic resonance. In fact, if it is roughly 2× the acoustic resonance, the peak voltage across the transducer can be greatly increased.".

I think I can take that at face value even though he doesn't reference a source. So according to his example:

1. Power supply = 5VDC
2. L1 = 3.2mHy
3. C(piezo) = 2nF
4. Signal source frequency = PZ1, resonant frequency = 40KHz
5. Signal source duty cycle is adjusted to eliminate a large current spike on turn-on

If I interpret this correctly, The mechanical (acoustic) resonance frequency is 40kHz so we would want to target an electrical resonance frequency of 80kHz. But if you do the math

so using his values of L=3.2mH and C=2nF
f=62850 Hz. - this isn't 80kHz.
But a few sentences down he says his oscilloscope shows, " * Violet = electrical resonance voltage across the transducer, 92Vppk. at 80KHz"

am I missing something?

fish