I have this same problem.
Videocard: Nvidia GTX 770 (4gb) with Driver: v.335.23
I think latest Nvidia driver (or FFXIV patch :P) caused this problem, because after I updated Nvidia these problems started. Going to test this out!
Most interesting part is that playing FFXIV causes computer (Videocard) to make low buzz/drone sound. Then I tried other game (in this case ARMA3) and there wasn't sound.