Probably intrinsic to the device.
Inside, there are copper coils that deliver the power, surrounded by ferrite ceramic pole pieces.
The coils can vibrate due to magnetic deflection. The ferrite can vibrate for this reason, as well as a material property (magnetostriction, a magnetic field <--> strain relationship).
There are also capacitors, which can vibrate for the same reason (except it's called electrostriction, and obviously, has to do with electric field instead), but that's not usually the culprit -- the above one is more common.
The operating frequency is typically low, for a variety of reasons (from electrical convenience to cost-effectiveness). One would hope they put it above 20kHz (where most people can't hear it), but it seems you got doubly unlucky with a noisy and lower-frequency unit.
Incidentally, magnetostriction is a square-law phenomenon, meaning, if the excitation is a 20kHz sine wave, you'd expect it to sing at 40kHz (because sin^2 x ~= sin 2x). The waveforms they are probably using, are too lopsided for this though, and you'll get some noise at the driven frequency anyway.
Tim