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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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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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blue_leaf77

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Evanescent wave which does not propagate also satisfies wave equation.

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Vanadium 50

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[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.

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Thanks.

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Generalizations are tricky.:)

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