You don't say what browser you are using and how that is configured. Some
people have it configured to have Mplayer or VLC play videos for example and
many people have Add-ons that may affect Flash. Also check the sound slider
below the Youtube video. Check other sites to see if this is a Youtube only
thing. Finally there is a separate Youtube Client in the repositories called
Minitube. You could install it and check to see if sound works in that or
try a different browser such as Chromium.