Jaunty fast then slow out of sync video with stuttering sound

Summary and description blatantly copied (and slightly modified) from the following discussion:

http://ubuntuforums.org/showthread.php?t=1146319

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The symptoms: this happens in mplayer and totem-xine and totem-gstreamer.

1) The video plays slowly with the sound out-of-sync with the picture
2) The video then plays REALLY fast to catch up with the sound
3) The sound stutters for a couple of seconds and then everything is in sync again for a few minutes
4) repeat from 1

This happens on most videos.
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I have this problem too after upgrading from Intrepid to Jaunty and thought that it might have to do with other issues I have with my ATI RC410 [Radeon Xpress 200M]. It seems that the problem is caused by something else, possibly by pulseaudio (as suggested by someone in the mentioned discussion).