Waves on a 1D string in higher dimensions, polarizations?

[Spinnor]

In 3 space dimensions consider a 1D string under tension between two fixed points. Let the string lie at rest on the z axis between z = 0 and z = ∞. We can produce linearly polarized and circularly polarized waves if I move the end of the string properly?

Now if we add an extra space dimension (but keep the string 1 dimensional) what additional types of wave polarization, if any, become possible?

If a string can vibrate in only one dimension we just get a wave. If a string can vibrate in two dimensions we get both linearly and circularly polarized waves. If a string can vibrate in three dimensions what does that lead to?

Thanks for any help!

 

[Spinnor]

+x,+y+w
+x,+y-w
+x,-y-w
+x,-y+w

Four types of polarization?

 

[Bill_K]

If a string can vibrate in two dimensions, that means the polarization vector is free to move on the circumference of a circle. It must have a periodic motion, so the possibilities are: a) remain still (linear polarization), b) rotate to the left, or c) rotate to the right. b and c are of course circular polarization.

If a string can vibrate in three dimensions, that means the polarization vector is free to move on the surface of a sphere. The possibilities are: a) remain still (linear polarization again) b) move on a great circle, or c) move on a small circle.