Diagnosis
The high-voltage diode or the magnetron's mounting is the likely source. A failing diode can cause a loud 60Hz hum. Loose magnetron mounting bolts cause vibration.
How to Fix It
Unplug the unit. Remove the outer case to access the component cavity. Visually inspect the magnetron's four mounting bolts. Check that they are tight. A loose bolt is the most common mechanical cause.
If That Didn't Work
The high-voltage diode may be arcing or failing. This requires a multimeter continuity test. A failed diode must be replaced. Do not attempt this without discharging the high-voltage capacitor first.
Heads Up
The cavity light and the turntable motor also make light operational sounds. The problematic hum is distinctly louder and often coincides with the magnetron's power cycle.