And yes, a video card with an HDMI port will definitely output sound along with video since that's what HDMI was designed to output.
Depends on the card. HDMI came out of the home theater (HT) world as an interface cable between totally separate
devices - A/V receivers, DVD/BluRay players, cable/DVR boxes - not just TVs.
HDMI is being "pushed" (shoved?) on to the computer world by the monitor makers (Samsung, Sony, Vizio, etc.) who just happen to be the same people who make big screen TVs. The makers are trying to save money by not having to design for, buy, inventory two connectors that do much of the same thing. And that is not a bad thing, but confusing just the same because in computers, most of those separate devices are inside the case and already interfaced via the motherboard and controlled by the OS (and not by HDMI control signals - as done by HDMI in HT systems).
Most computer monitors don't have internal speakers. And those that do sound lousy by any fidelity standard. So most computer users use computer speakers - often 5.1 or even 7.1 surround sound speaker systems with a big thumping subwoofer. Remember, for a graphics card to support audio, it must (1) provide pass-through support from an existing sound card (or integrated sound) or, it must (2) have an integrated sound controller on the graphics card - and most less expensive cards don't - almost all motherboards have integrated sound.
Also, many, if not most, computer monitors don't have pass-through support for audio either - since computer speaker systems (and headphones - and microphones too) need an input from somewhere too.
So it is common to run video out to a monitor via HDMI and run "normal" audio cables from the sound card (or the motherboard's integrated sound) to the speaker system (typically the subwoofer - which contains the powered amps).
From what I've read, in order to output sound using a DVI to HDMI adapter the DVI end of the adapter has to be DVI-D:
Ummm, again - not necessarily. DVI-D, as seen here
just means it carries digital video only. No "true" DVI format carries audio. However, both ATI and NVIDA have their own proprietary methods of pushing audio via DVD (typically over a DVD-D connector) with a special DVI to HDMI cable, but the display device must support audio (or audio pass-through) too.
There is no industry standard to push audio over DVI because HDMI is forcing DVI out of existence.
It's all confusing for sure. And will be until DVI fully phases out and HDMI is fully entrenched. But even then, full surround sound capability will have to come from somewhere. And while HDMI supports full 5.1 sound, it is not likely monitors will any time soon.
So there will still need to be a video cable out the monitor, and audio out to the speakers.
As for Monster Cables, I generally make every effort to stay miles away from them. They are WAY overpriced and have a history of poor - or rather downright shameful quality control. I would avoid the super cheap cables, but you don't have to buy the most expensive. For converting DVI to HDMI for video only, I would recommend simply an adapter
, then use a standard HDMI cable. Then run your normal speaker cables out to your speakers.