Substituting the plane wave solution into the wave equation

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SUMMARY

Substituting the plane wave solution into the wave equation involves applying the ordinary rules of differentiation, specifically the chain rule. The differentiation of the exponential function, expressed as (d/dx)e^(f(x))=(d/dx)(f(x))*e^(f(x)), is crucial for simplifying the equation. This process results in the cancellation of exponentials on both sides, leading to an algebraic relationship between angular frequency (omega) and wave number (k). For further understanding, reference any elementary calculus textbook for detailed explanations of these differentiation rules.

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  • Knowledge of ordinary differentiation rules
  • Proficiency in the chain rule of calculus
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  • Explore the relationship between angular frequency and wave number in wave mechanics
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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'.
 

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