There are two things making noise in the microwave when it’s running. There’s the transformer that’s making the high voltage for the magnetron, which is you 120 Hz noise you’re hearing.
The other noisy thing in the box is the fan. The fan is most likely a three blade metal fan running on a little shaded pole induction motor. That motor is very simple, just one moving part, and two poles. Two poles at 60 Hz gives us 3,600 RPM, which the motor can’t quite reach because as the RPM gets closer to that magic number of 3,600 rpm, the motor draws lesa current and makes less power. This difference between the speed the motor is trying to run (“syncronous speed”) and the actual speed is called the “slip” and is probably around 3%-5%. This gives us a fan speed between 3400 and 3500 rpm.
I don’t know if that is giving you the second noise you’re hearing, or if it’s mixing with the transformer noise to make it. But now you’ve caused a situation where I’m going to be caught holding a guitar tuner to my microwave.