Diagnosis
That's coil whine from the power supply board. It's common in LED TVs and is caused by electrical components vibrating at a high frequency. It's often more noticeable when the screen is very bright or showing a specific color.
How to Fix It
First, make sure the TV is plugged directly into a wall outlet, not a power strip or surge protector. Sometimes a poor-quality strip can cause noise in the power supply. If it's in a wall outlet, try a different outlet in the room to see if the buzz changes.
If That Didn't Work
Go into the TV's picture settings and try lowering the 'Backlight' level. High brightness demands more power, which can increase the whine. If lowering it from 100 to 80 makes the noise go away, you've confirmed the source.
Heads Up
While annoying, coil whine is rarely a sign of imminent failure. However, if the buzz ever changes to a loud hum, crackle, or you smell ozone, unplug the TV immediately. That indicates a failing component that could be a fire risk.