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Function for y(x,t) wave some questions

  1. Jun 29, 2011 #1
    1. The problem statement, all variables and given/known data
    A wave travels along a string in the positive x-direction at 33 m/s. The frequency of the wave is 48 Hz. At x = 0 and t = 0, the wave velocity is 2.8 m/s and the vertical displacement is y = 3 mm. Write the function y(x, t) for the wave. (Use the following as necessary: x and t. Assume x and y are in m, and that t is in s.)


    3. The attempt at a solution

    y(x,t) = Acos(kx - wt)
    should be the formula

    i'm assuming A = 0.003m but it is not so i don't know

    w = 2 * pi * f (frequency)
    = 2 * pi * 48Hz
    = 301.59

    k = w / v
    = 301.59 / 33(m/s)
    = 9.139

    so what i have now is y(x,t) = Acos(9.139x - 301.59t + something)

    how do i find the amplitude and the missing something if there is one?

    thank you
     
  2. jcsd
  3. Jun 29, 2011 #2
    your vertical displacement y(x,t) would be 3mm since at t=0 and x=0 , y=3mm

    y(x,t) = Acos( k(0) - w(0)) = A(1) = 3mm = 0.003m

    what you have looks right to me. Sorry if its not to clear, it's been a long summer
     
  4. Jun 29, 2011 #3


    one example was this question

    A wave travels along a string in the positive x-direction at 31 m/s. The frequency of the wave is 47 Hz. At x = 0 and t = 0, the wave velocity is 2.8 m/s and the vertical displacement is y = 3 mm. Write the function y(x, t) for the wave. (Use the following as necessary: x and t. Assume x and y are in m, and that t is in s.)

    the answer was 0.0099 * sin(9.53*x - 295.31*t + 2.84)

    i know how to get the k and w which was 9.53 and 295.31
    but i don't know how to get 0.0099 and 295.31 are
    thank you

    i know how to get the k and w which are 9.
     
  5. Jun 30, 2011 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Find the velocity of the piece of string at x=0, t=0, by taking the time derivative of your function. Then there two equations for the unknown amplitude A and phase constant (something:smile:)

    ehild
     
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