CaNaDan:
There is no such thing as a firewire to HDMI adapter. Since the video port on your iMac is a "mini displayport" or "mdp", I'll have to
assume you are using a mdp to HDMI adapter and a HDMI cable. Your HDMI cable cannot carry audio if the port is not providing audio.
The good news, your Mac will indeed pass audio through it's mdp. The bad news, there were no adapters or cables that also passed audio until 4-5 months after that model was released. So, if you bought the adapter during that period of time, or bought one of those adapters later, then you've got an adapter that does not pass audio.
If you happen to have an adapter that will pass audio, have you gone into System Preferences - Sound and selected the TV as the ouput? If this works, you can ignore the rest of the post.
If that didn't do it, you have a couple of options: replace the adapter you're using or add a separate audio cable.
You can grab
this adapter.
Or get a stereo miniplug 3.5mm cable like
this one and plug it in to the RGB/DVI audio port according to the diagram on pg 26.
(outdated image link removed)