Diagnosis
This is coil whine from the internal power supply components. It is a known issue, not a sign of imminent failure, but it is often caused by electrical noise on the circuit.
How to Fix It
First, unplug it from the wall outlet. Plug it directly into a different wall outlet, not a power strip or surge protector. Use the original power adapter that came with the unit. A clean, direct power source often eliminates the noise.
If That Didn't Work
The noise may be tied to its operational state. In the Ring app, go to the Chime Pro device settings. Tap on Audio Settings. Try toggling the Nighttime Quiet Mode on and off. A firmware change in its power management can sometimes stop the whine.
Heads Up
Do not attempt to open the unit. This will void the warranty and does not address the root cause. If the noise persists and is intolerable, contact Ring Support while the device is under warranty.