Power tools that run on AC are often series-wound motors. That is a type of motor called "universal" because it can run on DC or AC. If you have one that is small enough and an amplifier that is larger enough, the speed would be controlled by the amplitude of the signal from the amplifier.
If you also connect a speaker at the same time there will be loads of noise from the motor.
It is probably only the bass frequencies that would have an effect. Normal audio doesn't have a lot of power in the high frequencies, and the inductance of the motor windings will mean that the current will be less for the same voltage at high frequencies.
Please tell us what you are trying to do. If you have a particular application in mind, it might be better to process the audio signal and feed that into a motor controller.