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Trasverse wave wavelenght and velocity problem

  1. Dec 10, 2009 #1
    1. The problem statement, all variables and given/known data

    Along a long tense rope are traveling transverse waves with amplitude A= 10 cm. What is the wavelength, if at any given time the distance between two consecutive neighboring waves y= 5 cm is d= 6 cm? With what velocity are the waves spreading, if the maximum transverse speed of the rope is ω= 0.1m/s?

    2. Relevant equations

    v= fλ
    k= 2π/ λ
    y= A sin(k*x)

    3. The attempt at a solution

    For the wavelength:

    k= 2π/ λ → λ= 2π/ k

    Calculating k:

    y= A(sin k)(sin x) → sin k= y/ A(sin x)
    sin k= 5, which is wrong

    Where is my mistake?
     
  2. jcsd
  3. Dec 10, 2009 #2

    ideasrule

    User Avatar
    Homework Helper

    I don't understand what you did, but the equation for a wave is y=Asin(wt). (Note that the w here is different from the w in the question.) Derive that with respect to t and you get dy/dt=Awcos(wt), so Aw is the rope's maximum transverse speed. From there you can get the frequency, which you can then multiply by the wavelength to get speed.
     
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