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

  1. Feb 15, 2012 #1
    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!
     
  2. jcsd
  3. Feb 15, 2012 #2
    +x,+y+w
    +x,+y-w
    +x,-y-w
    +x,-y+w

    Four types of polarization?
     
  4. Feb 16, 2012 #3

    Bill_K

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    Science Advisor

    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.
     
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