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Find the speed of a transverse wave with one equation and three variables?

  1. Dec 17, 2006 #1
    1. Consider a transverse wave represented by the function
    y = 2.3 sin(1.9x - 25t)
    where y, x, t are in meters, meters, and seconds
    Determine the speed in m/s




    2. No relevent equations.



    3. I don't understand the way this problem is written. It seems like there are three variables with one equation, and I am supposed to arrive at a specific answer. Does anyone understand how to start this problem? Thanks very much for your help.
     
  2. jcsd
  3. Dec 17, 2006 #2

    OlderDan

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    What condition must be satisfied so that y has its maximum possible value? How does the position of that maximum depend on time? What does that have to do with the velocity of the wave?
     
  4. Dec 17, 2006 #3
    Hi OlderDan,

    Thanks for the help! Ok, I realize that what is inside the parentheses must equal pi / 2. And does that mean that the maximum y value is 2.3? I'm still not sure about the next part.

    Thanks
     
  5. Dec 17, 2006 #4
    If anyone else knows how to help with this, I would appreciate the help. I think that when 1.9x - 25t = pi/2, the maximum amplitude is reached, but I am not sure how to use this info.

    Thanks
     
  6. Dec 17, 2006 #5

    OlderDan

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    As time goes on, as it inevitably does, how does x have to change to keep 1.9x - 25t = pi/2? There is really nothing special about the value pi/2 in this question. Any constant value will do, so let's change the question to make it a bit easier. How does x have to change to keep 1.9x - 25t = 0?
     
  7. Dec 17, 2006 #6
    Ok, so as t changes 1, x must change 25 / 1.9 = 13.16? So the answer is x changes 13.16 m for every 1 s change in t.

    Is that correct? It seems right based on what you explained. Thanks again for all your help OlderDan.
     
  8. Dec 17, 2006 #7

    OlderDan

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    That will do it. If you want to go back to the y = maximum condition where you had 1.9x - 25t = pi/2, you can solve this equation for x and graph x vs t. The graph will be a straight line with slope = Δx/Δt = 25/1.9 with an intercept of pi/(2*1.9). The intercept is the position (actually one of many positions, but you only need one) of a peak of the wave at time zero, and the graph shows the postion of that peak as a function of time. The slope Δx/Δt = 25/1.9 is the velocity of that peak, and hence the velocity of the wave.
     
  9. Dec 17, 2006 #8
    Oh ok. I just did that in excel and it worked. Thanks again, that was interesting and very educational. I really gained some understanding from your help.
     
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