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String wavelength problem

  1. Nov 23, 2004 #1
    1) A cable made from a metal of density 8850 kG/cubic meter, and whose cross sectional area is 9.6 cubic mm is pulled to a stress of 103.4 Newtons. One end of the string is oscillated with a frequency 480.1 Hertz. The wavelength of the wave on the string (in meters) is

    T=f^2 * linear mass density * wavelength^2
    T=103.4 Newtons
    linear mass density = 8850 kG/cubic meter
    f=480.1 Hertz
    so, I plug all those in and got 2.25E-4
    but the correct answer is 7.27E-2

    The question gave a cross sectional area. How does that relate to the wavelength?
     
  2. jcsd
  3. Nov 23, 2004 #2

    Andrew Mason

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    I assume the cross-sectional area is 9.6 square mm, not cubic. The area is needed to calculated the mass per unit length of the string.

    The wave equation is given by:
    [itex]\lambda \nu = \sqrt {\frac{T}{M / L}}[/itex] where M/L = mass per unit length which is density x area

    [tex]\lambda = \frac{\sqrt{T/ \rho A}}{\nu}[/tex]

    [tex]\lambda = \sqrt{103.4/8850 \times 9.6 \times 10^{-6}}/480.1[/tex]
    [tex]\lambda = \sqrt{103.4/.08496}/480.1[/tex]
    [tex]\lambda = 34.886/480.1[/tex]

    [tex]\lambda = .0727 m[/tex]

    AM
     
  4. Nov 24, 2004 #3
    Thanks Andrew Mason!
     
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