I actually had a very similar problem back in 4.3.2, but I could work around this by disabling the "Ambient Sound" checkbox in the sound options. Unfortunately this does not work anymore now, and I'm stuck in a very unpleasant situation, as I rely on sound notifications to decrease the amount of visual notifications required.
It might also be relevant to note that I'm using muted sound files to silence a multitude of unwanted sound files (basically everything except boss emotes, the addon is here: http://www.wowinterface.com/downloads/fileinfo.php?id=18781), which has been working fine in every patch so far.
I know that the sound system has changed again in the latest patch, so that it only watches for .ogg files in the /Sound directory (and disregards any .wav files), but I'm not sure why this should affect other sounds not being played at all as well.
It almost seems as if the sound engine tries to play too many sound files at the sime time, chokes because of this and then simply drops certain sounds entirely (and even if the files are muted, they're still being played, you just don't hear anything).
I've also seen a thread in the US forum that seems to deal with a similar issue, but does not mention anything about additional sound files in the /Sound folder, so I'm pretty certain that this is a problem on Blizzard's end, and I hope for a quick fix (thread: http://us.battle.net/wow/en/forum/topic/4079846719).
I've tried to reduce the number of sound channels used from High (64) to Medium (32), and also activated the User Hardware checkbox, to no avail. Switching from 32bit to 64bit didn't help either.
Please, I could not stand to hear all that battle noise again, or having to completely disable the sound altogether.