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I How is the constant pi/L deduced in Fourier series?

  1. Apr 15, 2016 #1
    fourierSeries.png
    How is pi/L part deduced in (n*pi*x)/L?
     
  2. jcsd
  3. Apr 15, 2016 #2

    mathman

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    Essentially it has to do with the interval that the series is defined for. The length of the interval is 2L while [itex]\pi[/itex] is the normalization (based on the fact that sines and cosines have period [itex]2\pi[/itex]).
     
  4. Apr 15, 2016 #3
    We're requiring that the fundamental frequency is periodic in space, with spatial period ##2L##. So we have for the fundamental frequency: $$\cos \omega x = \cos(\omega(x+2L)) = \cos(\omega x + 2L \omega) \Rightarrow 2L \omega = 2\pi \Rightarrow \omega = \frac{\pi}{L}$$
     
  5. Apr 15, 2016 #4
  6. Apr 16, 2016 #5
    Thank you guys, I understand now.
     
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