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How is pi/L part deduced in (n*pi*x)/L?

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How is pi/L part deduced in (n*pi*x)/L?

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henry wang said:

How is pi/L part deduced in (n*pi*x)/L?

We're requiring that the fundamental frequency is periodic in space, with spatial period ##2L##. So we have for the fundamental frequency: $$\cos \omega x = \cos(\omega(x+2L)) = \cos(\omega x + 2L \omega) \Rightarrow 2L \omega = 2\pi \Rightarrow \omega = \frac{\pi}{L}$$

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Thank you guys, I understand now.

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