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Wave second order derivative equation

  1. Feb 7, 2015 #1
    Whenever the second order derivative of any physical quantity is related to its second order space derivative a wave of some sort must travel in a medium, why this is so?
  2. jcsd
  3. Feb 7, 2015 #2


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    Evanescent wave which does not propagate also satisfies wave equation.
  4. Feb 7, 2015 #3

    Vanadium 50

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    It's not so.

    [tex]\frac{\partial^2 u}{\partial t^2} = v^2 \nabla^2 u[/tex]

    is a wave, but

    [tex]\frac{\partial^2 u}{\partial t^2} = -v^2 \nabla^2 u[/tex]

    is not. The solution of the top equation is in sines and cosines, and the second is sinh and cosh.
  5. Feb 8, 2015 #4
  6. Feb 8, 2015 #5
    And this is just for a linear relation. They can be "related" in more complicated ways.
    Generalizations are tricky.:)
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