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Homework Help: Wave Equation

  1. Mar 16, 2007 #1
    1. The problem statement, all variables and given/known data

    The displacement of particles in a string stretched in the x direction is represented by y. Which of the following expressions for y describe wave motion:

    1: cos kx sin wt
    2:[tex]k^2x^2-w^2t^2[/tex]
    3:[tex]cos^2(kx+wt)[/tex]


    2. Relevant equations

    Equation of a progressive wave is of the form [tex]y=f(t-\frac{x}{v})[/tex]


    3. The attempt at a solution

    The first equation represents a standing wave. The second obviously cant be it (its not of the form f(t-x/v) ). But I thought the third one would represent the equation of a progressive wave. It doesnt though. Why?
     
  2. jcsd
  3. Mar 16, 2007 #2
    x'=-x
    wt+kx=w(t-k/w x')=w(t-x'/v)
    (using v=w/k)
     
  4. Mar 16, 2007 #3
    Yeah. I got that. But it isnt the answer. The third equation doesnt represent a wave. Why?
     
  5. Mar 16, 2007 #4
    Why not?

    cos^2 (wt-kx')=1/2+1/2cos(2[wt-kx'])
    w'=2w
    k'=2k

    so the fn=A+Bcos(w't-k'x')

    Looks like a sinusoidal wave to me.

    What's wrong with using a standing wave? Isn't that what you'd get in a stretched string?
     
  6. Mar 16, 2007 #5
    Yeah, you get a standing wave cause of superpoosition in a string. The thing is, that only one answer is correct. Maybe the language points to a standing wave?
     
  7. Mar 16, 2007 #6
    You get a standing wave, because the string is stretched- so it must be held at both ends.
     
  8. Mar 16, 2007 #7
    If a string is stretched, it doesnt necessairily mean that you would have to get a standing wave.
     
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