Why do lighting dimmer switches emit audible noise sometimes at very high frequencies despite the fact that home electrical service is just 60 Hz AC?
You are hearing on of the harmonics. Most dimmers are triac based, and simply turn on at a certain point in the AC wave. This sharp change in voltage induces noise into the system, often causeing the filiments of lights to resonate at certain settings. You are hearing something resonating at a harmonic because of a cheap dimmer.