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Finding the equation of a wave. ?Easy?

  1. Jun 30, 2011 #1
    1. The problem statement, all variables and given/known data

    A wave travels along a string in the positive x-direction at 34 m/s. The frequency of the wave is 49 Hz. At x = 0 and t = 0, the wave velocity is 2.3 m/s and the vertical displacement is y = 5 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.)


    2. Relevant equations

    sinusoidal wave:
    y = Asin(kx+wt+phi)


    3. The attempt at a solution

    I'm trying to understand all of this. I really don't though. I believe the y displacement has something to do with amplitude, correct? Why is there 2 different wave velocities?
    If anyone could give me a nudge in the right direction, I'd really appreciate it.
     
  2. jcsd
  3. Jun 30, 2011 #2
    Well, let's start with what we're given:

    [itex]\begin{align} v &= 34 m/s \\
    f &= 49 Hz \\
    y(0, 0) &= 5 mm \\

    y(x, t) &= A\sin{kx + \omega t + \phi} \end{align} [/itex]

    However, this just gives us the displacement of the wave in the y-direction as a function of position in the x-direction and time. There is additional information given, and that has to deal with velocities. What's the relationship between position and velocity, and how can we use that relationship to help solve this problem?
     
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