DIAGNOSIS Coil whine from the power supply board. A component is vibrating at high frequency.
FIX Unplug the TV from the wall for 2 minutes. Plug it directly into the wall outlet, not a power strip or surge protector. A poor power source can excite the coils.
IF THAT DIDN'T WORK The noise is coming from a specific inductor or transformer on the power board. It's not a safety hazard, but it is annoying. You can try to dampen it with a non-conductive epoxy, but this requires opening the TV and locating the exact component.
HEADS UP If the buzzing changes pitch or is accompanied by a burning smell, unplug immediately. That indicates a failing capacitor, which is a fire risk.