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Homework Help: Traverse Wave on a String

  1. Dec 7, 2011 #1


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    1. The problem statement, all variables and given/known data

    In a demonstration, a 0.45 kg horizontal rope is fi xed in place at its two ends (x = 0 and x = 5.0 m) and made to oscillate up and down in the fundamental mode, at frequency 4.0 Hz. At t = 0, the point at x = 2.5 m has zero displacement and is moving upward in the positive direction of a y-axis with a transverse velocity of 5.0 m/s.

    (a) What is the amplitude of the motion of that point?
    (b) What is the wave speed in the rope?
    (c) What is the tension in the rope?

    2. Relevant equations

    3. The attempt at a solution

    I already found to amplitude to be .199 m by taking the derivite of the wave equation and solving for A.

    For part B, though the wave speed would simply be wavelength*frequency, but 20m/s is not the correct answer. I tried to mess around with a few other equations but they led me nowhere.

    And for part C I know T is simply (v^2)*μ, but I obviously need to first find velocity.

    Any help would be grealty appreciated, thanks!
  2. jcsd
  3. Dec 7, 2011 #2
    What value did you use for the wavelength. The vibration is the fundamental which means the string is half a wavelength long .
  4. Dec 7, 2011 #3


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    Alright so the speed should equal ((wavelength*freq)/2), or (5*4)/2 , which is equal to 10 m/s? That answer doesn't work for me either.
  5. Dec 7, 2011 #4
    First of all : you know the frequency is 4Hz and the wavelength is (2 x 5) =10m.... this gives you the speed (v = fλ)
    Speed = sqrt (T/μ) .....you should be able to get T ???
    The amplitude is given by a SHM equation. Max velocity in SHM = ωA = 2∏fA
    The midpoint of the string is doing SHM with max amplitude....
    Hope this helps you to finish it.
  6. Dec 7, 2011 #5


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    Alrigh I finally got it, I was dividing by 2 instead of multiplying by it. Thanks for your help!
  7. Dec 7, 2011 #6
    Great... well done
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