DVI to HDMI connection - but no sound

I had a problem connecting my Vista PC to my LCD HD TV using the DMI
connections on both (the TV's DMI connection was flakey) and so purchased a
DVI to HDMI cable, connecting the DVI output of the PC to the HDMI input of
the TV.

This works fine - for video - but I get no sound.

I appreciate that my PC's DMI output does not carry a sound signal but I
haven't touched the PC audio out to my TV audio in connection - which worked
fine when it was DMI to DMI but is now silenced when it is DMI to HDMI. How
come?

Is there a fix - or have I wasted my money buying this new cable?

Cheers.

Bobby