You can find everything beautifully explained in this website on brass instruments: https://newt.phys.unsw.edu.au/jw/brassacoustics.html

A short version is that for ultrasonic (>20 kHz) vibrations you would need to increase the air pressure made by the mouth. That can be done by either putting more air through the mouth or making the volume through bigger. Alternatively, you could think of the "embouchure" being very tiny to make the pressure very high (I will do some quick math here and assume a linear relationship between the pressure and with a typical value of 1kPA to make a trumpet sound around 1kHz, maybe 20 times the pressure will lead to ultrasonic soundwaves).

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8313787/ Here you can see that the damage threshold of the tympani is around 30-100 kPa, so I would speculate that you would need to apply such an absurd amount of pressure to whistle ultrasonically that you would rupture your timpani at the same time.

I am neither a clinical expert or acoustics expert, so those numbers are just from "fun" calculations based on the linked evidence, but I hope there are more publications about what is the true range that a person can actually achieve "humanly".