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I am designing a controller to cut down heat production in electrically actuated solenoids (12VDC, 10A). This is not for proportional control. I am using a 50% duty cycle and have been experimenting with frequencies. I have tried 60, 120, and 500HZ. In each case, I am hearing a hum that increases with frequency. I understand the concept of magnetostriction, however when I remove the coils I still get the hum suspended in air with no ferromagnetic material nearby. I have read several similar questions but most boil down to magnetostriction which can't be the case here. Despite the hum, the solenoids perform fine at any of the three frequencies.

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Wires carrying current create a magnetic field, which applies force to other wires.

The sound is motion due to Lorentz force. The parallel coil windings of the solenoid attract each other (and the coil diameter increases slightly) at twice the frequency of the current through the windings. If it is bothersome, vacuum impregnation of the windings (filling the gaps between wires with varnish) can reduce the sound.

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