Diagnosis
That's coil whine coming from the internal power components. It's an electronic noise, not a mechanical one, and it's a known issue with some units. It's often more noticeable in a very quiet room.
How to Fix It
First, try a different power outlet in a different room to rule out electrical noise from your home's wiring. If the noise persists, the most effective fix is to swap the power adapter. Use the original Motorola-branded power brick and cable that came with the camera. If you've lost it, order an official replacement. Third-party chargers, even if they fit, can cause or exacerbate this whine because they don't regulate power as cleanly.
If That Didn't Work
If you're using the original adapter and it still whines loudly, the issue is likely inside the camera unit itself. Contact Motorola support. They are aware of this fault, and if your unit is under warranty, they will often replace it. Be prepared to send them a short audio clip of the noise.
Heads Up
A very faint hum or buzz when the night vision LEDs are active (in a dark room) can be normal, but a loud, piercing whine in a lit room is not. Don't try to open the unit yourself to fix it, as you'll break the tamper seals and void any warranty.