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I agree with Nick's original point about the mains motor. Compared to the cheap and lightly constructed DC motors that replaced them, the AC motors were often sturdy and long lasting, but induced hum, especially when located close to the head.

I had a nice dual capstan early Akai model but I felt the hum, probably even from new, was unacceptable. That was even with a factory fitted hum shield around the motor.

As an elimination test you could try temporarily shielding the play head by holding a piece of suitable metal in front of it to see if that reduces the hum.