I noticed this when initially Youtube wouldn't play sounds, but iTunes etc would.
I then restarted my comp and Youtube started working but BlackOps still doesn't play any sounds, I've put them on the loudest possible, different output options and all that and no result =/
Please help =]
This has nothing to do with COD:BO, I doubt you will find help to your issues here, try entering in a question into your favorite search engine.
It may surprise you that it is more effective than posing in a games forum.
(if you are having sound issues in BO I am sorry and below is a good fix)
1. Open the game
2. Go to settings, change to windowd mode (this should allow you to see your taskbar)
3. Open the sound options, you should see a listing for COD:BO
4. clicky on the slider and turn up volume there
I had an issue that sound worked, but not for Black Ops, this fixed it for me. Hope it helps