Hey. I bought a HDMI to DVI-D cable.

If my computer has a DVI slot like so:
http://www.blogeek.ch/images/test/XPS2010/19.jpg

Then can I use a HDTV (that has HDMI obviously) to use as a monitor?

DVI is for visual data. If I plug in speakers in the computer and turn off sound on the HDTV, would the sound go through the speakers?