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Homework Help: Traveling Wave Model: transverse wave on a string

  1. Jun 24, 2010 #1
    1. The problem statement, all variables and given/known data
    A transverse wave on a string is described by the wave function: y=(0.120m)sin([tex]\frac{\Pi}{8}[/tex]x+4[tex]\Pi[/tex]t) Determine the transverse speed and acceleration of the string at t=0.200s for the point on the string located at x=1.60m. What are the wavelength, period, and speed of propagation of this wave?


    2. Relevant equations
    vy= -[tex]\omega[/tex]Acos(kx-[tex]\omega[/tex]t)
    Since f=[tex]\frac{1}{T}[/tex] and [tex]\omega[/tex] is 4[tex]\Pi[/tex] does that mean T=0.500?


    3. The attempt at a solution
    I was able to come up with -1.51 for the transverse speed, and I am pretty sure I understand why the acceleration is 0. I am having problems coming up with the wavelength and the proagation speed.
     
  2. jcsd
  3. Jun 24, 2010 #2

    Doc Al

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    Staff: Mentor

    Yes.

    Hint: How does k relate to the wavelength?
     
  4. Jun 24, 2010 #3
    Hi Doc,

    I had tried [tex]\lambda[/tex]= [tex]\frac{k}{2\Pi}[/tex] with k=frac{\Pi}{8} and it didn't work out to the right answer.
     
  5. Jun 24, 2010 #4

    Doc Al

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    Staff: Mentor

    What wavelength did you get?
     
  6. Jun 24, 2010 #5
    I got .0625m and the book says it should be 16m
     
  7. Jun 24, 2010 #6

    Doc Al

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    Staff: Mentor

    That should be k ≡ 2π/λ.
     
  8. Jun 24, 2010 #7
    So how does that change the relationship between k and [tex]\lambda[/tex]? I couldn't write it as [tex]\lambda[/tex]= [tex]\frac{k}{2\Pi}[/tex]?
     
  9. Jun 24, 2010 #8

    Doc Al

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    No. If [itex]k = 2\pi / \lambda[/itex], then [itex]\lambda = 2\pi / k[/itex]. (Just algebraic manipulation--but make sure you understand it.)
     
  10. Jun 24, 2010 #9
    Oh alright I've got it now. It's those silly little math mistakes that get me every time. Thanks much Doc.
     
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