Its for S Video, which is a Analogue connection which does not carry sound.
I have seen that some of these cards come with DVI to HDMI adaptors. I know the ATI cards convert the sound and so can carry Audio over the HDMI.
I dont know if the Nvidia cards do the same or if you need to run additional sound.
Mactronix
 


You do not need to get a DVI to HDMI cable since the monitor you picked is a computer monitor and has a DVI port. Just use the DVI cable that is included with the new monitor to connect the monitor to the graphics card.

You would only want to get a DVI-to-HDMI adapter if you decided to hook up an LCD *television* monitor to your computer as LCD TVs have speakers and often lack DVI input. HDMI is simply DVI plus audio, and since you use headphones, you don't need any monitor to get a sound signal.
 
HDMI and DVI are both digital interfaces. Any digital interface will give you either a perfect signal or obvious artifacts like pixelation. As long as you have a cable with intact wires and don't get one that is overly long (don't worry, you likely won't run across a cable that's too long), you'll get a perfect signal with either interface.