I have a fractal design integra 650 watt 80+ bronze psu, and when I had a gtx 650 in my PC, I had no coil whine. I upgraded to a gtx 770 several months ago, and I am plagued with extremely loud coil whine that changes in pitch when I move in games. I put one of my friend's gtx 660s in my PC to test something, and when I started a game, The same sound came from the 660. My friend said he wasn't sure if his 660 made that noise before, but I'm not sure that it is a coincidence. Is it the psu that is causing the whine, or another component? I'm aware that these things have natural coil whine, but to have the same exact grating/whining noise when ever I play games is making me want to replace the gpu or the psu...Or im crazy.
Are you sure it's coming from your computer, and not your speakers? It could just be a shielding issue with an audio cable either caused by something internal (GPU most likely given the symptoms, but PSU is also possible) or your monitor/monitor cable. It could also be coil whine as you suggest, maybe caused by the PSU reving up to deliver more power to the GPU... Since it persisted when you tried another GPU, I doubt replacing it would help. If your buddy has a suitable PSU you could test, it might be worth a shot (or try your GPU in his rig etc), and see if it is your PSU that is the root cause. Testing, testing, data, data. Need more data. ; )
Either way, I doubt it's anything to worry about besides being annoying.
Thanks, I wear headphones, and I wasn't wearing them when I heard the screeching noise. I got really close to my psu to test your theory (It was very intimate) and the sound is indeed emitting from the GPU. Very similar to this---------> https://www.youtube.com/watch?v=HP73edpQwgc