One of my bigger quads, and my little 150mm copter had a really high-pitched squeal at certain RPMs of the motor. At first, I thought it was the bearings, so I changed the bearings in the motor that made the most noise, but the noise persisted!
I put an oscilloscope on the motor leads and found that the frequency the ESC fed to the motor was around 3Khz. But that is a square wave, meaning that there would be substantial harmonic power at the 3rd harmonic - 9KHz. I think that is the squeal that I heard. I can still hear 9Khz if it is very, very loud. I can imagine what some youngster would think!
So why do some motors produce noise at high audio frequencies, while some do not? Is it the motor "bells". I put some silicone seal (a pretty good sound dampener) on the outside of the motor and did my best to balance the weight to see if that made a difference. It did not. If it wasn't the motor bell, what was it?
So I took the motor apart and figured out what was going on - the windings were loose!!! The copper wires in the coils themselves were moving ever so slightly back and forth in response to the driving current and making the noise. I realized immediately that this is a VERY bad situation, since the wires will constantly bend back and forth (even if only a fraction of a thousandth of an inch) and eventually work-harden and break. That could put your expensive toy on the ground in a hurry.
I wanted to hold the wires in place, and thought epoxy might be a good choice, but I didn't want to block the space between the windings - that is needed for cooling airflow. I was looking for something really thin that would adhere to the wires via capillary action. I found something - superglue (ethyl cyanoacrilate). It worked perfectly when dripped over the top of the windings. It wet the wires and embeded itself into them, then hardended. The only downside is that 150C is the maximum temperature. I don't know if the insides of my motors ever get that hot, but maybe they do.
So, after super-gluing the coils, I put the motor back together and let the glue harden for an hour or so. Then I powered it up.
So far, so good. And I'm looking for some suitable glue that has a higher temperature rating. If anyone knows of one, I'd like to hear from you.