making a dc motor sing under load
The ability of a motor-driven assembly to "sing" will depend in substantial measure upon the construction of the drivetrain, the amount of stall torque available, and the thermal characteristics of the motor.  In some cases, the amount of heat that can be dissipated in the windings of a motor which is driven with a square wave when one is trying to make it "sing" can exceed that of an immobilized motor which is fed constant DC of the same magnitude, and depending upon gear construction and backlash the voltage required for a 400Hz square wave to destroy a motor may be lower than the voltage required to make a readily-audible 400Hz noise.

I would guess that a typical toothbrush which is run by a DC brush motor will probably use plastic gears in its drivetrain.  Plastic gears often have a small amount of elasticity which is good for longevity and smooth operation, but which would likely absorb much of the audio-frequency energy you might try to put through them.  You could try driving the toothbrush with an AC waveform and see what happens, but it may be impossible to get good audio coupling.