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Transverse Speed of a particle on a wave

  1. Apr 29, 2009 #1
    1. The problem statement, all variables and given/known data
    The equation of a transverse wave traveling along a very long string is given by y = 6.0sin(0.012pi*x + 4.9pi*t), where x and y are expressed in centimeters and t is in seconds.

    Find the maximum transverse speed of a particle in the string.


    2. Relevant equations



    3. The attempt at a solution
    I want the speed, or rate of change of position, or derivative of position. The given equation represents the transverse displacement, so, at t = 0, I would have y' = 6*0.012picos(0.012pi*x). Since y(x, t) is a sine function, the greatest slope would be at (0, 0), so y'(0, 0) would represent the greatest rate of change of y(x, t).

    So the maximum transverse speed of a particle in the string would be 6*0.012*pi, correct?

    This, however, is not the right answer, so why not?
     
  2. jcsd
  3. Apr 29, 2009 #2

    rl.bhat

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    Homework Helper

    You have to take the derivative with respect to time.
     
  4. Apr 29, 2009 #3
    The speed is the time derivative.
     
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