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How can i tell if an expression represents a traveling wave?

  1. Sep 21, 2008 #1
    1. The problem statement, all variables and given/known data

    psi(x,y)= Asin((ax^2)-(by^2))

    Does this expression represent a traveling wave? If so what is the direction and speed of the wave?

    2. Relevant equations
    This wave resembles a a harmonic wave.

    psi(x,t)= Asin(kx-wt+phi)

    3. The attempt at a solution

    Ok, A,a,b are constants. I do not think this expression represents a traveling wave because the argument of the sin function is to the second order. For an expression to represent a traveling wave does the expression have to be to the first order, or only a certain part of the expression.

    1. sin(x+y)^2
    2. sin^2(x+y) does these represent traveling waves?

    1 has the argument squared. if we multiply out the argument is no longer linear, and thus not a traveling wave?

    2 has the entire function squared, is this a traveling wave?

    What are some characteristics of traveling waves, mathematically?

    Thank you.
     
  2. jcsd
  3. Sep 21, 2008 #2
    [itex]kx-\omega t=0[/itex]

    [itex](kx)^2-(\omega t)^2=0[/itex] too.

    [tex]k=\frac{2\pi}{\lambda}[/tex]

    [tex]\lambda=\frac{v}{f}=\frac{2\pi}{k}[/tex]

    [tex]f=\frac{\omega}{2\pi}[/tex]

    You can solve for v in terms of a and b using the above, but it assumes that y is analogous to t.

    Regards,

    Bill
     
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