Hi there,
from what you describe it seems it is a coil whine. It's nothing you should be worried about since it doesn't make smoke or smells like burning. Google it for more info.
On the other hand, it might be a special work schedule for the fans. That's why the sound is repeated.
Let me know if you found the problem as I'm planning to buy a new GPU and this one is on my watchlist.
Cheers