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I don't think that there's any fundamental reason that an induction cooker needs to be doing anything around 20kHz. I'd guess that it's just the power supply happening to be flipping power on and off at that frequency.
You could probably just get a different cooker.
I've got two, I've had 3 in the past. They all do it. I have no idea what the frequency is other than "painful and barely audible"