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A standing wave on a string with a mass hanging on it

  1. Nov 30, 2011 #1
    1. The problem statement, all variables and given/known data
    A sphere of mass M=6.85 kg is supported by a string that passes over a light horizontal rod of length L=0.73 m.

    Given that the angle is θ=22.3° and that the fundamental frequency of standing waves in the section of the string above the horizontal rod is f=246 Hz, determine the mass of this section of the string.

    2. Relevant equations
    v = √(T/μ)
    μ = m / L
    v = fλ

    3. The attempt at a solution
    First off, I found the length of the string by using trig since it's a right triangle. L = 0.789 m (different L than on the attached picture)

    It is the fundamental frequency so the λ = 2L. λ = 1.57 8m

    The tension I found through looking at its FBD from which I obtained T = mg/sinθ. T = 177.09 N

    Now I combined eliminating v from two of the equations above, I derived fλ = √(T/μ). Then I substitute μ = m / L and isolate m. I get an equation of m = (TL/[fλ]^2)

    Using the derived equation, I calculate a value of m = 0.000927 kg, but the CAPA says it is wrong. I was quite confident on my approach, to the point that I'm doubting the CAPA now, so I don't know where my errors are.
     

    Attached Files:

  2. jcsd
  3. Dec 1, 2011 #2
    The tension in the string is not mg/sinθ
    it's just mg as the string passes over a (I presume) smooth end of the rod.
    Otherwise the method is correct.
     
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