I'm not familiar with soundManager (I'm guessing it's a plug-in), but many audio players have event listeners built in. You could investigate the soundManager documentation, see if it has an "onuadioended" (or similar) event, and when that fires, call a function to run your video
[EDIT]: If this is the same one you're using, the onfinish event at this link may prove useful:
http://www.schillmania.com/projects/soundmanager2/doc/