Diagnosis
This is coil whine from the monitor's internal power supply or voltage regulators. It is a physical characteristic, not a defect, but its audibility varies by unit and ambient noise.
How to Fix It
The whine often correlates with brightness. Open the Picture menu and adjust Brightness down from 100. Test at 80, 60, and 40. The noise frequency and volume will change. Find a brightness level where it is inaudible in your environment.
If That Didn't Work
The whine may be exacerbated by a specific input signal. Switch from DisplayPort to HDMI or vice-versa. Also, try setting the refresh rate to 60Hz instead of the default 75Hz via your computer's display settings to see if it changes.
Heads Up
Coil whine does not indicate impending failure. It is not covered under warranty unless deemed excessive. If the sound is a loud buzzing or crackling, that is different and may indicate a faulty component.