Not to repeat what's on the web but as long as you stay on HDMI it should be 30Hz. Gamers tend to move the GPU back to 1080p and let the TV upscale since gaming on even the 280x may not get enough frames per second (unrelated to display rate.)
There is something bothering me lately About how to connect a future 4k monitor using high speed hdmi cable with Ethernet and enjoying 60hz.
first: my GPU is Radeon™ R9 280X GAMING 3G which has 2 displayports 1.2, and one hdmi 1.4a .
One of my possibilities is Philips BDM4065UC, which Supports 4K res with any HDMI but only at 30hz, while display port 1.2 has 60hz.
the problem is that I already planted an HDMI cable in the wall so display port is not an option now.
what can I do to gain the 60hz? is it possible to bring a DP 1.2 adapters to HDMI ? to use on both sides? (the GPU and TV) will it be the same?