Note: No, there are no inverters involved in this question here.
I've perceived that most, if not all induction motors make a "howling" sound in their coils that is different from the constant 60 Hz tone they produce due to the working frequency.
This howl has pitch shifts depending on the rotor speed. In very low speeds it is low-pitched and blends with the 60 Hz hum, but as it speeds up the sound evolves into higher pitches. When accelerating I can hear it standing out when it gets around ~100 Hz and then it starts getting quieter after reaching ~400 Hz. When decelerating it does the opposite (I start hearing at ~400 Hz and then it goes down until it blends with the 60 Hz hum).
I have the impression that in motors with more poles this sound is much more audible, like my 16-pole ceiling fan motor. In it the howling is very audible when its spinning at low speeds, like 60 RPM.
And the more "effort" the motor is doing the louder the howl, reversing the fan during operation makes a much louder howl just before reversing (while it's at a low speed and decelerating, nearly stopping) than just after reversing.
I've also heard that howl in several other induction motors, most of them being 4-pole motors. The motors in vertical washing machines, for example, make a quite audible howl when accelerating (in the centrifugation step).
I know that this is probably the result of the interaction between the applied Electromotive Force and the Back Electromotive Force induced on the stator windings, as they're not in-phase and the speed of the rotor modulates the back-EMF on the stator windings.
The resultant between the EMF and the back-EMF (and the successive iterations of inductions between the stator and the rotor) might produce a higher frequency signal on the windings.
However, I can't figure out exactly how this happens.
Does anyone know how can I model the process making that sound?