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Derivation of wave equation using tension of a string

  1. Dec 15, 2015 #1
    1. The problem statement, all variables and given/known data
    I'm currently following the textbook Advanced Engineering Mathematics by Erwin Kreyszig.

    I'm learning the derivation of the Wave equation using the method shown in the book, but when I reached the final part of the derivation, the working just confuses me.

    (1/Δx)[ (u/dx)| x+Δx - (du/dx)| x ] = (p/T) ( second derivative of u wrt t )

    at this part, it mentions that we are taking the lim ∆x→0, which will end up in the wave equation.

    2. Relevant equations
    (1/Δx)[ (u/dx)| x+Δx - (du/dx)| x ]

    3. The attempt at a solution

    I've tried working out the limit, but I guess there's something I don't know since as Δx approaches zero, the derivative terms will become the same and cancel out each other?
     
  2. jcsd
  3. Dec 15, 2015 #2

    DrClaude

    User Avatar

    Staff: Mentor

    $$
    \lim_{\Delta x \rightarrow 0} \frac{f(x + \Delta x) - f(x)}{\Delta x} = \frac{df}{dx}
    $$
     
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