Nodes on a Vibrating String

  • Thread starter MyNewPony
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  • #1
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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?
 
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Answers and Replies

  • #2
Borek
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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.
 
  • #3
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Think of the properties of the sine function (which is the shape of the string with the given boundary conditions.)
 
  • #4
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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.

Wavelength = (2/n)*length of string

Can I get a hint on what to do next?
 

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