Depends on the circuit, but magnetostriction is a common cause for circuit noise. That is, if the power is high enough, the physical shape of the part changes according to the magnetic field strength.
The same thing can happen under the influence of electrical fields.
Also, if you can hear it, the sound is below 20 kHz - the frequency of the sound may give you a clue what is causing the noise. If it is a low hum, it could be 120 Hz AC line transformer hum, or switching power supply hum, etc.