Basically, the previous answer about capacitors is right, but here's the thing - the beeping might depend on the volume precisely because the power supply is getting more load. When the sound is louder, the amplifier draws more power, and if there's a faulty component in the PSU, it starts beeping more intensely. It's not dangerous for the TV in terms of explosions or short circuits, but it sounds awful.
Capacitors typically don't fail within six months under normal operation, so it's most likely a manufacturing defect or factory flaw. I wouldn't recommend opening the TV yourself - there's high voltage in the power supply, and if you do find something, you could desolder it wrong and end up with serious problems. Especially since the warranty should still be valid if you bought it half a year ago.
Call LG service and describe the problem - they'll most likely replace the PSU under warranty for free, or swap out the whole TV if they have one in stock. They usually don't make a fuss about this kind of thing when the device is new.