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

  • Thread starter Jen C
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  • #1
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Homework Statement


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


Homework Equations


Kx=n * pi


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
 

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Answers and Replies

  • #2
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hey i cant see the picture>?
 
  • #3
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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.)
 
  • #4
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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
 
  • #5
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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.
 
  • #6
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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?
 
  • #7
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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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