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Wave equation variables.

  1. Nov 7, 2009 #1
    I am unable to determine the relationship between x and t in the following equation.

    [tex]
    y\left(x,t\right)=A\sin\left( kx-\omega t \right)\\
    [/tex]


    If [tex] \nu=\frac{x}{{t}}[/tex] then the numbers within the bracket goes to zero; because [tex] kx=\omega t [/tex]
    for all points on y(x,t).

    Can anyone enlighten me please?
     
  2. jcsd
  3. Nov 7, 2009 #2
    x and t are independent variables; there is no relationship between them. That equation describes a wave. Pick any time t_0, then you can look at the whole wave in space (along x). Pick a point x_0, and you can see how that point oscillates in time. Both can be looked at independently.
     
  4. Nov 7, 2009 #3
    I set-up a spreadsheet and generated a sinusoidal wave starting at x0 which progresses parallel along the positive x-axis.
    If I leave t=0, then any value I plugged in for x falls on the curve.
    Likewise, if I left x=0, then any value I plugged in for t falls on the curve.

    Does this mean when one variable has a value then the other must be 0?
     
  5. Nov 7, 2009 #4
    No. It's a wave function of two free variables, x and t--longitudinal position and time. Pick any constant t and you have a standing wave at t. Let t be a variable to see the evolution of the wave over time.
     
    Last edited: Nov 7, 2009
  6. Nov 15, 2009 #5
    I had trouble grasping the concept of how to graph a function depended on two variables. I found a site that presented a simple Gaussian wave and then progressed to a Gaussian Wave dependent on two variables. The page wraps up with a general equation of a cosine function dependent on two variable including axes offsets.

    I found it to be a great site for explaining the implication of a function with two independent variable. Now I understand a little better what is happening in the wave equation.


    http://resonanceswavesandfields.blogspot.com/2007/08/true-waves.html
     
  7. Nov 15, 2009 #6
    In 3D space a function of two variables can be drawn as a surface, wavy in both directions in your case.
     
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