You are correct in that the low frequencies are the most problematic, and the most difficult to mitigate, as they have long wavelengths and more energy. However, even 2kHz. is a coincidence problem with common sheathing. Buzzes and rattles can happen at most any frequency. Just a quarter wavelength can excite a resonant frequency.
Think also of electronics being sensitive to vibrations, and then amplifying them into the system.
Think also of how little mechanical energy it takes to cause havoc. For example, take a music box mechanism and play it the air. You are primarily hearing the resonance of the bedplate. Now couple it to the wall and play it. You’ll hear about a 27 dB increase. The tines are moving +/-0.1 mm and are causing the wall to move a few billionths of a meter. About 100,000 times less movement, with an intensity factor increase of about 300. Note also that the tines are playing from about 400 Hz. and up.