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Homework Help: Given velocity of a transverse wave, need to find w and k. Please help!

  1. Apr 25, 2010 #1
    1. The problem statement, all variables and given/known data
    The drawing shows a snapshot of a transverse wave traveling along a string at 8.8 m/s. The equation for the wave is y(x, t) = A cos (wt + kx).



    (a) Is the wave moving to the right or to the left?
    To the left

    (b) What are the numerical values of A, w, and k?
    A 2 mm,
    w rad/s
    k rad/m

    (c) At what times could this snapshot have been taken? (Give the three smallest nonnegative possibilities in order.)
    ms ms ms


    2. Relevant equations
    Kx=n * pi


    3. The attempt at a solution I found the amplitude to be 2mm but I am not really sure where to go from their. I tried solving for w with the velocity but it doesn't give you frequency or wave length. Please help I am lost!

    Sorry I just attached a picture of the graph
     

    Attached Files:

    Last edited: Apr 25, 2010
  2. jcsd
  3. Apr 25, 2010 #2
    hey i cant see the picture>?
     
  4. Apr 26, 2010 #3
    For part (b), I found k first. Then used that to find w.

    k=2pi/wavelength

    then

    w=kv (v given in word problem)

    If you or anyone has insight about part (c), that's where I'm at. (I actually got 2 and 3, but 1 is coming back incorrect for me.)
     
  5. Apr 26, 2010 #4
    I am not sure how to get the wave length. I found the amplitude to be 2mm but I am not sure how to solve from their
     
  6. Apr 26, 2010 #5
    When I look for wavelength, I'm a peak-to-peak kind of guy. Just read the x-axis and see how far apart they are. Looks around .04m.
     
  7. Apr 26, 2010 #6
    For any physics masters out there, this is what I've tried for part C:

    Part C: (c) At what times could this snapshot have been taken? (Give the three smallest nonnegative possibilities in order.)

    y(x, t) = A cos (wt + kx)

    1. took an (x,y) coordinate from graph (peak 1): (0.03m, 0.002m)
    2. plugged into equation along with values found in part B, and solved for t at each cycle
    y(x, t) = A cos (wt + kx)
    0.002m = 0.002m cos ((1382 rad/s)(t) + (157 rad/m)(0.03m))
    1 = cos ((1382 rad/s)(t) + (157 rad/m)(0.03m))

    Point 1:
    2pi = ((1382 rad/s)(t) + (157 rad/m)(0.03m))
    t=1.4ms

    Point 2:
    4pi = ((1382 rad/s)(t) + (157 rad/m)(0.03m))
    t=5.68ms

    Point 3:
    6pi = ((1382 rad/s)(t) + (157 rad/m)(0.03m))
    t=10.2ms

    Points 2 and 3 give me a correct answer. Point 1, incorrect. I've tried rounding differently and such. But it's just not happening. Anyone see any error in my logic/work?
     
  8. May 4, 2010 #7
    Your answer for 1 is correct you just had one more decimal place than needed when i calculated it with your equation I came up with 1.1 and thats the correct answer
     
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