DIAGNOSIS Coil whine from the internal power supply components, specifically from the inductor coils on the main board. This is a physical characteristic, not a defect, but can worsen with age or dust.
FIX Clean the router's vents and ensure proper cooling. Power off and unplug the router. Use compressed air to blow dust out of all ventilation slots. Place the router upright on its stand in a well-ventilated area. The change in thermal load can sometimes alter the resonant frequency of the coils, reducing the noise.
IF THAT DIDN'T WORK The noise is inherent to the electrical components. You can try placing the router inside a well-ventilated cabinet to dampen the sound. Replacing the external 12V 3.5A power adapter will not fix this, as the whine originates internally.
HEADS UP While annoying, coil whine does not indicate imminent failure or affect performance. However, if the noise suddenly changes to a loud buzz or crackle, immediately unplug the device as this could indicate a failing capacitor.