Try reinstalling your motherboard's onboard sound drivers, as the sound is actually produced by a different piece of hardware than the HD4290 it is hooked up to. The GPU is only for the images, but the PC combines the two devices output for the HDMI connection.
If the new drivers don't help, try using the onboard sound with another type of device (like PC speakers) to see if the problem happens there as well. If PC speakers have the same issue, there may be a hardware issue with the onboard sound. If the PC speakers don't have the same problem, then it might be the HDMI cable, though it was my understanding that HDMI cables either work or they don't. I am no expert on HDMI, so take this with a grain of salt.
I have only experienced this once on a 785g motherboard a few months ago (HD4200 onboard) and there was no resolution to be found. It happened right out the box and I had to exchange the board. The replacement board did not have the same issues.