DIAGNOSIS That's coil whine. It's coming from the internal power supply components and is a physical, not software, issue. It's most noticeable in a very quiet room.
FIX First, check if it's related to brightness. Go to Settings > Display and crank the brightness all the way up and then all the way down. Sometimes the whine changes pitch or stops at a certain level. Find a brightness setting where it's least noticeable or gone and leave it there. If that doesn't help, try plugging it into a different wall outlet, preferably on a different circuit. Poor or 'dirty' power can exacerbate coil whine.
IF THAT DIDN'T WORK If the noise is loud and constant and the above steps don't change it, you're likely dealing with a faulty component. Since this is a known but sporadic issue with some units, your best path is to contact Google Support. They may determine it's a defect and offer a replacement if the device is still under warranty.
HEADS UP This noise is generally harmless and doesn't indicate a safety issue, but it can be irritating. It's not something you can fix by cleaning or a software update.