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Vibrational modes of a discrete particle string

  1. Nov 20, 2013 #1
    I just want to make sure I understand the normal modes of a vibrating system of particles with discrete spacing. I have tried to drawn what I understand as the lowest and highest frequency mode of the standing waves. Is the drawing correct? Edit: actually I have drawn the maximum frequency where no particles are permitted to move..
    The system is 4 particles and for standing waves their vibrations are described by:
    y(s) = sin(sKa) with a time dependence and where s refers to particle number s and a is the particle spacing.
    Now with y(0)=y(4) you have the modes:
    k=[itex]\pi[/itex]/4a, [itex]2\pi[/itex]/4a, k=[itex]3\pi[/itex]/4a
    The last one corresponds to no movement of any particle. Is this correctly understood? What happens if we take for instance k=[itex]5\pi[/itex]/4a. Does this mode simply reproduce the motion of k=[itex]\pi[/itex]/4a?
     

    Attached Files:

  2. jcsd
  3. Nov 20, 2013 #2
    I'm not sure that I understand your question exactly. If you are just trying to understand how standing waves work then it is easier to think of just 2 points which are the ends of a "string". The string must always be anchored to these two points, so the minimum energy mode is a half wave. There is no maximum frequency in the simplest models. The more vigorously you shake the string, the greater the frequency of the standing waves.

    Have a look at this picture from wikipedia
    http://en.wikipedia.org/wiki/File:Harmonic_partials_on_strings.svg
     
  4. Nov 20, 2013 #3
    It is standing waves but not on a string, rather for a system of particles with a discrete spacing. Like when you examine vibrations of atomic planes.
     
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