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Wave on a string under tension

  1. Mar 9, 2012 #1
    1. The problem statement, all variables and given/known data
    A pulse takes 0.1s to travel the length of a string. The tension in the string is provided by passing the string over a pulley to a weight which has 100 times the mass of the string.
    What is the length (L) of the string?
    What is the equation of the third normal mode.

    2. Relevant equations
    v=√(F/u) u=m/L


    3. The attempt at a solution
    We have L/t = √(100.m.g/(m/L) where g = surface gravity

    So 100L^2 = 100gL
    so L= magnitude(g) = 9.8 m

    This type of question was not covered directly in our notes and I am unsure if my working is correct.
    Thanks for any help.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 9, 2012 #2

    Simon Bridge

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    Welcome to PF.
    Reasoning seems fine to me - notice how the number end up all nice?
    Did you do the next bit?
     
    Last edited: Mar 9, 2012
  4. Mar 9, 2012 #3
    It was the simplicity in the final answer that made me doubt it.
    Thank you, but what is LQ?

    y_3 = (A_3)sin(n.pi.x/L)cos((w_n)t)

    We have 1.5 waves in a time of 0.1s. So w = 30.pi radians
    I don't see how I can get the amplitude.

    So y = A sin(3.pi.x/9.8)cos(30.pi.t)
     
  5. Mar 9, 2012 #4
    (where w is angular frequency)
     
  6. Mar 9, 2012 #5

    Simon Bridge

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    A spelling mistake. Thanks.

    angular frequency is radiens per second.
    me neither.
    I suppose with all the computer-randomized problems you get these days, nice numbers must be rare.

    Note: cannot comment on answers as such - only methods and reasoning.
     
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