Wave second order derivative equation

  • Thread starter shiromani
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Main Question or Discussion Point

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?
 

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  • #2
blue_leaf77
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Evanescent wave which does not propagate also satisfies wave equation.
 
  • #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.
 
  • #4
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Thanks.
 
  • #5
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And this is just for a linear relation. They can be "related" in more complicated ways.
Generalizations are tricky.:)
 

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