DIAGNOSIS This is coil whine from the internal power supply components. It is a known physical characteristic of some units, not a sign of malfunction. The sound may fluctuate with network load.
FIX Confirm the sound is coil whine and not a fan (the Nest Wifi Pro has no moving parts/fan). If confirmed, mitigation is physical. Ensure the router is on a hard, flat, ventilated surface. Do not place it on fabric or inside a cabinet. Try plugging it into a different power outlet on a separate circuit to test for clean power.
IF THAT DIDN'T WORK The whine may be more noticeable in a very quiet room. If the sound is exceptionally loud or changes to a crackle, it indicates a defective power adapter. Contact Google support for a replacement power adapter.
HEADS UP Coil whine does not affect performance, speed, or lifespan. Attempting to open the sealed unit to address it will void your warranty.