Diagnosis
This is coil whine from the monitor's internal power supply or inverter. It is a common physical characteristic, not a functional defect. The pitch may change with screen brightness.
How to Fix It
Lower the monitor's brightness setting. Navigate to Menu > Picture > Brightness. Reduce it from the default 100 to 70 or 80. This reduces electrical load on the components causing the noise. Also, ensure the monitor is plugged directly into a wall outlet, not a power strip with other high-draw devices.
If That Didn't Work
The whine may be exacerbated by a specific refresh rate. In your graphics card control panel, try changing the refresh rate from 100Hz to 60Hz to see if the noise diminishes.
Heads Up
This noise does not indicate impending failure. However, if the buzzing becomes a loud crackle or pop, or is accompanied by a burning smell, disconnect power immediately as this indicates a component failure.