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Wave equation

  1. Nov 25, 2009 #1
    In the wave equation u(x,t), what does u represent?
     
  2. jcsd
  3. Nov 25, 2009 #2
    Can you write out the equation?
     
  4. Nov 25, 2009 #3

    LCKurtz

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    If you are representing a vibrating string, then u(x,t) represents the displacement of the string at location x at time t.
     
  5. Nov 25, 2009 #4
    yungman: u''(t)=u''(x)c^2

    lckurtz: so visually its like a plane/surface in 3D (x,y,z) where x = x, y = t and z = u ...?
     
  6. Nov 25, 2009 #5

    LCKurtz

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    I would visualize x to the right, u vertically, and motion in time. You can see a gif on my home page: http://math.asu.edu/~kurtz" [Broken].
     
    Last edited by a moderator: May 4, 2017
  7. Nov 25, 2009 #6
    Anyone else so visually its like a plane/surface in 3D (x,y,z) where x = x, y = t and z = u ...? !
     
  8. Nov 25, 2009 #7
    I don't think so, From your equation, it gives the wave is travelling in x direction only. I assume t is time, x is the distance. I think you switch x and t also. It should be u"(x)-(c^2)u"(t)=0.

    If you want direction in x y and z, you have to use Laplace equation to have PD of all three direction:
    [tex]\nabla[/tex] [tex]^{2}[/tex]u - C[tex] ^{2}[/tex][tex]\frac{d^{2}u}{dt^{2}}[/tex] = 0

    I can't get the equation look right, I hope you get what I mean!!!!


    So I look at your equation as the function u(x,t) ( of x direction and time t ) travel in x direction with the magnitude of the function u(x,t). "c" is the velocity.

    This is a one dimension spacial problem of x.
     
    Last edited: Nov 25, 2009
  9. Nov 26, 2009 #8

    HallsofIvy

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    Your original equation did not have a "y" variable so you can think of z as either the height of a string in one-dimension or as the height of a "cylindrical" wave, extending infinitely in the y direction. In any case, your original "u" is the height of the wave if you are thinking of a physical wave, the intensity if you are thinking of a light wave, etc.
     
  10. Dec 1, 2009 #9

    jvc

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    Actually, u is complex amplitude of the wave, which denotes the amplitude of given spatial point and time. So u represents the wave field distribution in space.
     
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