Sorry, but everyone needs to get their facts straight.
The op in this thread has stated his Mac has mini-DVI.
Suggesting or referring the op to use an adapter that will not even plug into the port on his Mac does no one any good and only confuses others that find this thread looking for mini-DVI connections that have no knowledge about all the varied video adapters / cables that are in use now.
On to the original question, sorry, but you also are mistaken. Brairden has it correct.
While it is true that HDMI can carry both audio and video, it has to be connected to a port that also carries both audio and video. DVI and/or mini-DVI is a video only specification and has never had the ability to carry audio whether on a Mac, a Windows machine, a Linux rig or anything else you can name.
If you need specific recommendations for adapters and cabling, you will need to provide the info requested in the first post
here.
(edit: it's not meant to be as gruff as it sounds upon re-reading. There is just a lot of mis-information and half information related to this topic all across the web.)