The only semblance of a part-solution which kind of worked
for a couple people would require you to either:
1 — fool around with your "registry" (which I would be totally
against because that could really screw up your computer);
2 — download some utilities (which I would be just as much
against, because that kind of stuff is what probably created
your problem in the first place).

Thus, my first piece of advice is to shutdown then reboot. If
that doesn’t work, clear your "cache" of "Cookies", "History"
and "Temporary Internet Files", thus making your computer
"fresh" in YouTube’s eyes. My infamous "CHTIF" triple-cure
has resolved hundreds of YouTubers’ problems. So why not
yours. Please reboot after doing this:

Internet Explorer 6:
→ Tools → Internet Options
→ Delete Cookies → OK
→ Delete Files → OK
→ Clear History → Yes
→ OK

Internet Explorer 7:
→ Tools → Internet Options → Delete…
→ Delete files → Yes
→ Delete cookies → OK
→ Delete history → OK
→ Close (browsing history window)
→ OK

Mozilla Firefox 3:
→ Tools → Clear Private Data
[x] Browsing History
[x] Download History
[x] Saved Form and Search History
[x] Cache
[x] Cookies
→ Clear Private Data Now

To clear your "cache" within IE 8, Safari, or Google Chrome,
please check out this other "Best Answer" of mine:
http://answers.yahoo.com/question/index?qid=20090604145307AAPbGic

If that does not do the trick, here’s some other suggestions:

♦ If this just happened to you, there’s one person on Yahoo
who discovered their own solution by going back to the last
video they watched that had sound. See "Additional Details":
http://answers.yahoo.com/question/index?qid=20090913084412AAqVE5q

♦ If you’ve got "accelerators", get rid of them because most
of them conflict with YouTube. "Ad Block" and "Messenger"
programs also interfere with YouTube.

♦ There could also be conflicts with other video players that
are installed on your computer, like Windows Media Player,
Real Player and QuickTime. Check all of their volumes, too.

♦ The newer versions of Flash are frustrating a whole bunch
of YouTubers. Most updates are typically good for only one
thing: software conflicts. If you are using 1 of the 8 versions
of Flash 10 (yes, there actually are 8), you should consider
the Asker’s comments on this other "Best Answer" of mine:
http://answers.yahoo.com/question/index?qid=20081125075929AABZpVS

♦ Some people found success by just closing their browser
and restarting it. A couple others rebooted, and one person
wrote to me recently saying that everything started working
magically again the next day with no effort on his part; thus
your problem might just be a temporary glitch.

If you’re able to determine the "cause" and its "cure", could
you please click my avatar and let me know — so that I can
include it in my future Yahoo! Answers. One other apparent
cause so far seems to be if you download "Torrents" music.

I wish you the best of luck and hope that there’s something
in my long answer that will do the trick for you.

Here are 2 other possible solutions to videos with no sound.
They might seem old but they both got very positive results:

FIREFOX + VISTA:
zarin denatrose . wordpress . com / 2008 / 07 / 31 / fixing – sound – firefox – vista /
http://zarindenatrose.wordpress.com/2008/07/31/fixing-sound-firefox-vista/

WAVEMAPPER:
www . my digital life . info / 2007 / 08 / 15 / adobe-flash – no-sound – wavemapper-trick /
http://www.mydigitallife.info/2007/08/15/adobe-flash-no-sound-wavemapper-trick/
References :