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Waves: fundamental frequency of taut cable

  1. Dec 16, 2016 #1
    1. The problem statement, all variables and given/known data

    The wire cable supporting the mast of a sailboat has a length of 12 m and a linear mass density of 350 g/m. When pushed sideways at its midpoint with a force of 160 N, the cable deflects by 9.5 cm. What is the frequency of the fundamental mode of vibrations on this cable?

    2. Relevant equations
    λn.fn=v and velocity:v=sqrt(T/μ) , lemda λn=2L/n and L= length of string
    fn=n/2L . sqrt(T/μ)
    fundamental≡ the first mode ⇒ n=1
    3. The attempt at a solution
    for n=1
    f=1/(2*12) .sqrt (160/0.35) =0.89 Hz
    but it is incorrect why??
     
  2. jcsd
  3. Dec 16, 2016 #2

    Merlin3189

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    Gold Member

    In the equation you use, what are each of the terms? ( IE. what do the letters f, n, L, T and μ stand for?)
    Which of these are given?
    What other information are you given?
    How will you work out the term, which is not given?

    As a hint, you don't use one of the given values and you mis-use one of the given values.
     
  4. Dec 16, 2016 #3
    T=tension=160N
    μ=linear mass=0.35kg/m
    f is the frequence
     
  5. Dec 16, 2016 #4

    Merlin3189

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    Gold Member

    The tension should be the tension in the cable.
    The value 160N is the force used to displace the cable sideways by 9.5cm.
    The tension in the cable would be much greater. (A mast over 12m high would hardly be supported by a tension of 160N on each side.)

    So you need to see how you can use the information given, to calculate the tension in the cable.
     
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