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Nodes on a Vibrating String

  1. Sep 22, 2010 #1
    Prove that there are n-1 nodes on a string fixed at both ends for the nth harmonic.

    It is simple to show this using a diagram.

    [PLAIN]http://www.space-matters.info/img/nodesandmodes.jpg [Broken]

    However, is there a way to show this mathematically?
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 23, 2010 #2


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    Staff: Mentor

    You probably have to go through the harmonic frequencies and harmonic wavelengths - once you have wavelength and you know how it depends on the initial length of the string, the rest should be obvious.
  4. Sep 23, 2010 #3
    Think of the properties of the sine function (which is the shape of the string with the given boundary conditions.)
  5. Sep 24, 2010 #4
    Wavelength = (2/n)*length of string

    Can I get a hint on what to do next?
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