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Max. speed of particle on wave

  1. Sep 15, 2007 #1
    1. The problem statement, all variables and given/known data

    Progressive waves are generated on a rope by vibrating vertically the end, P, in simple
    harmonic motion of amplitude 90 mm. The wavelength of the waves
    is 1.2 m and they travel along the rope at a speed of 3.6ms–1. Assume that the wave motion is not damped.

    Calculate the maximum speed of point P.



    3. The attempt at a solution

    The actual solution is V=2(pi)xfxA
    Since f=v/wavelength= 3.0 Hz and A=90x10^-3m the answer is 1.70 m/s

    I don't understand why this formula is used and where the 2pi has come from. Is it to do with simple harmonic motion? I would be very grateful if someone could help with a derivation of the formula.
     
  2. jcsd
  3. Sep 15, 2007 #2

    learningphysics

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    What is the general equation of a wave?
     
  4. Sep 15, 2007 #3
    equation

    v=f lambda???
     
  5. Sep 15, 2007 #4

    learningphysics

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    Have you see this equation before:

    x = Acos(kx - wt)
     
  6. Sep 15, 2007 #5
    oh gosh no I haven't! erm on my physics data sheet there's a similar equation: x=Acos2Pift. hmmm I'll see what comes up when I google the equation you just gave me! Thanks
     
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