High School String oscillations, not parallel to momentum?

[Spinnor]

I there a simple hand waving explanation why strings "can oscillate in any spatial direction except parallel to momentum" (quote from below). I assume the yellow arrows below represent momentum.

Edit, why not parallel to momentum?

From an interesting read on the electron,

http://motls.blogspot.com/2013/01/evolving-portrait-of-electron.html#disqus_thread

Thanks!

 

[jerromyjon]

why not parallel to momentum?

I think the black line represents the "momentum" and the yellow arrow is the direction of the "orbit", so the closed string is only free to fluctuate in other directions, not in the "main" momentum loop.