There are many reports of coil whine with GTX 970 cards than ever before. These coils are in the power delivery and regulation circuitry. When the components are pushed hard, they start to vibrate to a level it is audible, especially if they are not high grade components. But it is weird that this is happening with cards as power efficient as GTX 970s, because there are many cards that draw more than 100W more power but without claims of coil whine.
When I bought my MSI GTX 970 Gaming graphics card, I hoped that it would be free of coil whine too. This is because it is using a custom PCB with very high quality components. Alas, there is coil whine. It is not very distracting or pronounced, however it is there...again, not all the time but at very random occasions; not even when it is under very high load either.
I tried capturing it on audio but it was extremely difficult to capture anything useful because of the noise from the other fans inside the case. However I found a video posted by someone on YouTube demonstrating coil whine on his Asus Strix card but that was way extreme compared to my case. I don't hear that level of coil whine. One might even call mine as having no coil whine at all. But I still hear it and it is a extremely distracting when it is there. Plus, I didn't pay for it in the first place. In fact, I paid more not to have it. Plus, there are people claiming that the little hum that their cards originally put out eventually became an irritation as they decided to stick even when the card was loaded properly.