Coil whine is a bad thing and makes me unhappy.
Use the EVGA Precision software to limit frame rate and coil whine will become less.

4 out of 4 have it now... Took three back that had coil whine. I now tried an ACX, coil whine too. It has the least for sure. The ASIC quality is 64 on this one though, the last one I had was 74%.

I just registered here to provide some info that hopefully will help you folks troubleshoot more accurately. I don't know if there is a problem with your EVGA cards or not, but I do know concretely that the Corsair AX series power supplies (and perhaps others in their line) suffer from well documented cases of coil whine. Just go Google "AX860 coil whine" or your model # and the words "coil whine."
 
While some amount of coil whine cases are to be expected from any large volume PSU manufacturer, a quick comparison of similar searches on other brands will show that these cases are far fewer in quantity and that the Corsair PSU's are troublesome. This is pretty surprising since the PSU is actually a Seasonic, which usually means quality but you cannot ignore the many pages of forum complaints in regard to this issue.
 
As for why you are just hearing it now? Well if you're upgrading from a different generation GPU (or upgrading multiple components at a time) you are likely adding more load to your PSU. It makes perfect sense then that you might attribute this whine to the latest component you added (your new EVGA card, for example) when in actuality the fault lies with your PSU. In browsing this thread it seems like the commonality is in fact a Corsair AX PSU. 
 
Like I said at the start, I cannot claim the EVGA card isn't at fault - I don't know that. However I can certainly steer you in the right direction if you want to troubleshoot the issue and if you have a Corsair PSU that is exactly where I would start. Somewhere else in this thread a guy suggested using a cardboard tube (like an empty paper towel roll) to help you isolate where sound is coming from. That might be an excellent way to get a better reference of where the noise is coming from.
 
Good luck - please let me know if this was helpful or if you were able to isolate the issue. FYI if you are looking for a great PSU, I recommend the Antec HCP-850 Platinum or anything else well reviewed by jonnyguru.com.

stickywulf
Coil whine is a bad thing and makes me unhappy.
Use the EVGA Precision software to limit frame rate and coil whine will become less.

that dont help, it even dont help a bit. This coil whine nowadays is not only in benchmarks where do u have a lot of fps like 200-300, the coil whine which i have now is in games, where i have under 40 fps. Iplayed ac 4 or tomb raider with max sttings and during the whole time coil whine, fps limter or vsync dont help. I tested allready 6 differnts gtx 780 ti with 3 differnt PSU, and the result is they coil whine all, some a bit more then the others but in the end they coil whine all. A lot of people dont notice that maybe because of loud fans or a silent case or maybe the case is 2 meters away from u. But if u have ur case on ur desktop like me its a pain in da ass

Here is an interesting find. I put the stock cooler back on, stuck the card in my girlfriends PC and the card is not as loud albeit still noticeable. I tried switching the power supply and it's still REALLY loud in my personal PC. I am thinking it could just be me due to how loud her CPU fan is but I really think it is quieter.

Taking a fourth crap card back tomorrow. I will stick with my 780 that doesn't whine at all. 

opps!

I started running  yesterday and that is when I noticed it, a very high pitch whine, it doesn't do it on any other games only Star Trek Online which I don't know why it only does it on that specific game but I hardly play that.
 
If I turn down the power target to 60% in EVGA Precision X I still get the whine but its so quite that you really have to listen for it and when I have my headphones on there is no way I would be able to hear it. Because it nearly goes away when I turn the Power Target down that is leading me to believe its my PSU, I have a OCZ ZX Series Gold Rated 1250 watt PSU. I upgraded from SLI 560 Ti's the Saturday after Xmas, so I've had the Card for about 2 weeks.
 
I don't want to go through an RMA and get another card that could possibly have a high coil whine, that's even if it is the card.

I had a 780 classey and reg 780, and I have a new 780 Ti, it all whines.... and I have corsair HX 1050 Gold..

All,
 
I figured out how to get rid of coil whine, it has to do with the fan speed of your CPU, just set it to normal in BIOS. It worked for me....

For those that are using an EK block and back plate for their WC setup.  I found the buzzing/whining to be caused by my back plate.....I used the small plastic washers that were for the block installation and placed them under the screws for the back plate.  After a couple RMA's this turned out to be the solution for me.  Guessing something on the EK back plate is just a tiny bit off in manufacturing?  Either way.....it fixed my issue.  Good luck!!