Your experience sounds much like my own. I had coil whine on my card EVGA gtx 670 FTW when i first got it; it was audible particularly during benchmarking tests (like ungine heaven), and the first games I tried to play. Switching V-sync on on the games got rid of it though. It was particularly noticeable, at the time, on really graphically light games; the kind where it says you're getting over 1000 fps before you turn v-sync on.
I think the problem itself may have also decreased over time as well, as now, it's really only for the first minute or so of a benchmarking type program, and then it goes away (which coincides with a stabilizing of the card's power usage and GPU usage).
So, to sum things up; coil whine is sadly not that unusual with graphics cards in certain situations. If V-sync doesn't solve the problem, try turning on a frame limiter as well (via your favorite software program like afterburner); that can occasionally help. People have different opinions as to whether coil whine is a justified reason for an RMA; in my personal opinion, if it was substantially impacting my enjoyment and use of my card (it is a horrible sound after all) I would probably have to RMA it. Thankfully I didn't have to in my case, as V-sync took away virtually all the problems.
I'm not too sure about the particular noise you're hearing on Bioshock Infinite though, sadly...