Substituting the plane wave solution into the wave equation

janemba
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what do you have to do to solve this

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Try substituting the plane wave solution into the wave equation.
 
And what rule do you use to do that
 
You use, like, (d/dx)e^(f(x))=(d/dx)(f(x))*e^(f(x)). The ordinary rules of differentiation. Just tell us what you get. The exponentials should cancel on both sides leaving you with an algebraic relation between omega and k.
 
is there like a video that teach you the rules of ordinary rules of differentiation ?
 
I don't know that there is a video, but try any elementary calculus text. Pay particular attention to the 'chain rule'.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.

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