4th gen ipod nano makes buzzing sound through headphones only off the charger.

4th generation iPod makes strange buzzing sound through the headphones only when it is off the charger. When the iPod is charging, the buzzing sound goes away.

I have left the iPod on until the battery dies, charged it all the way back up, restored it and still get the buzzing sound only when the iPod isn't charging.

Any ideas what this could be and what I can do to fix it?