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Question about waves (velocity, tension)

  1. Mar 9, 2013 #1
    1. The problem statement, all variables and given/known data

    Two steel wires are stretched with the same tension. The first wire has a diameter of 0.580mm and the second wire has a diameter of 0.88mm. If the speed of waves traveling along the first wire is 54m/s, what is the speed of waves traveling along the second wire?

    2. Relevant equations
    v=sqrt.(F/miu) (miu is mass/length)


    3. The attempt at a solution
    I tried to make a proportion. 0.58/54=0.88/x. I got the incorrect answer, though. The answer should be 35.6m/s.
     
  2. jcsd
  3. Mar 9, 2013 #2

    rude man

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    Why a proportion? That is not the formula for speed of waves in a wire with linear density μ under tension F.
     
  4. Mar 9, 2013 #3

    mfb

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    There is a square root in the equation. Density (mass/length) is proportional to the squared velocity, not the velocity itself.
     
  5. Mar 9, 2013 #4
    Okay, but then what should I do?
     
  6. Mar 9, 2013 #5
    I know. I put the formula as v=sqrt. (F/miu)
     
  7. Mar 9, 2013 #6
    Oh alright I see what you are saying. So a proportion is not the way to go here. But what should I do? I feel like I'm missing the information. Don't I need force or mass?
     
  8. Mar 9, 2013 #7

    rude man

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    v = sqrt(F/μ) is correct. Did you still not get the right answer? Are your units consistent?
     
  9. Mar 9, 2013 #8
    I don't think I am solving it right
     
  10. Mar 9, 2013 #9

    mfb

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    A ratio is a good idea, but you cannot use the velocity directly, you have to use the squared velocity (=a quantity proportional to μ).
     
  11. Mar 9, 2013 #10

    rude man

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    What did you get for v?
     
  12. Mar 10, 2013 #11
    You are on the right track. The mass per unit length is PRORTIONAL to the diameter squared.
    The mass per unit length of the 0.88mm dia wire is (0.88/0.58) squared = 2.3
    Use this in your equation for speed (dont forget the square root !!!!) and you should get 35m/s
     
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