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Simple Wave Problem

  1. Sep 22, 2009 #1
    1. The problem statement, all variables and given/known data
    Monochromatic transverse wave is propagating
    in the positive x direction on a string (neither end is fixed).
    The wave velocity is 12 m/s, amplitude 0.05 m, and wavelength is 0.4 m.
    At t=0 and x=0 the string altitude is 0, and moving in
    the positive y direction [i.e. (dy/dt)|(t=0) > 0]

    Find the altitude y at x=0.25 m and t=0.15 sec.

    3. The attempt at a solution
    I figured that since y is 0 when x and t are 0, it must sine:
    y(x,t) = Asin(kx-ωt)

    I found the parameters I need:
    k = (2π/λ)=(2π)/(0.4) = 5π
    ω = vk = 12*5π = 60π

    and I get
    y(x,t) = 0.05sin(5πx-60πt)

    I plug in the values x=0.25 and t=0.15 and get
    y(0.25,0.15) = -0.02

    But this is not the answer. Why?
    What did I do wrong?
     
  2. jcsd
  3. Sep 22, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Gil-H! Welcome to PF! :wink:
    The wave equation looks ok, :smile:

    but how did you get .02? :confused:
     
  4. Sep 22, 2009 #3
    I got -.02 because I was unawarely working in degrees.
    I should be .0354
    But after advice I got, I changed the wavefunction to be:
    y(x,t) = -0.05sin(5πx-60πt) (I added a minus sign)
    That's because of the condition that (dy/dt)|(t=0) > 0.

    Anyway, thanks for trying to help (-:
     
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