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Wavelength problem

  1. Mar 2, 2013 #1
    1. The problem statement, all variables and given/known data
    A uniform string of length 0.5 m. is fixed at one end and free at the other end. Find the wavelength of the fundamental mode of vibration.


    2. Relevant equations
    λ = (2L) / mode


    3. The attempt at a solution
    λ = (2(0.5 m.)) / 1
    λ = 1 m.

    But the solution says it's 2 m. because λ = 4*L. Why is it 4L when the formula is 2L?
     
  2. jcsd
  3. Mar 2, 2013 #2

    Delphi51

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    Homework Helper

  4. Mar 2, 2013 #3
    I don't understand why the fundamental is 1/4 wavelength in my problem. Maybe it might help if I understood where the formula λ = (2L) / mode came from, because it's the only one involving wavelength and length that I know.
     
  5. Mar 2, 2013 #4

    Delphi51

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    I have not seen λ = (2L) / mode but it suggests a string fixed at both ends:
    Then mode = 1 would be one wavelength spread over two lengths or half a wavelength on the string length L. At mode = 2, a complete wavelength on the length L. If you draw pictures of these, you'll see that both ends of the string are fixed in each case. See http://www.phys.unsw.edu.au/jw/strings.html.
     
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