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Wave Velocity: Improper approach, or incorrect differentiation?

  1. May 29, 2012 #1
    1. The problem statement, all variables and given/known data

    A transverse wave on a cord is given by D(x, t) = 0.19sin(2.9x - 35t), where D and x are in m and t is in s.
    1) At t = 8.6*10^-2 s, what is the displacement of the point on the cord where x = 0.62 m?
    2) At t = 8.6*10^-2 s, what is the velocity of the point on the cord where x = 0.62 m?

    2. Relevant equations

    given displacement ---> D(x, t) = 0.19sin(2.9x - 35t)

    3. The attempt at a solution

    I didnt have any trouble finding the displacement of the wave along the cord (-0.18m) as all I had to do was plug in the given values of x and t, then make sure my calculator was in radians.

    The velocity is where I ran into problems. I figured it shouldnt be any harder than taking the derivative of the given equation, then once again plugging in the supplied values. However, I did not come up with the correct answer, and I not sure if I simply differentiated incorrectly or if that is not even the correct approach. Heres my work:

    0.19sin(2.9x - 35t) ---> ∂D/∂t = 0.19cos(2.9x - 35t) * (2.9 - 35t)
    ∂D/∂t = 0.19cos(2.9x - 35t) * (2.9 - 3.01) = (-0.11)*0.19cos(2.9x - 35t)
    ∂D/∂t = -0.0209cos(2.9x - 35t)
    ∂D/∂t = -0.0209cos(-1.212)
    ∂D/∂t = -0.007338 m/s

    But, like I said, ∂D/∂t =/= -0.007338 m/s

    Any help would be greatly appreciated.
     
  2. jcsd
  3. May 29, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Try this derivative again. Review the chain rule.
     
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