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Representation of waves as sum of sine/cosine waves
Build I(x) of wave components e^{ikx} = \cos kx + i\sin kx :
I(x) \approx \sum_{k\in K} b_k e^{ikx}
- k is the frequency of a component ( \lambda = 2\pi/k corresponding wave length)
- K is some set of all k needed to approximate I(x) well
- b_k must be computed (Fourier coefficients)
Since u(x,t)=\half I(x-ct) + \half I(x+ct) :
u(x,t) = \half \sum_{k\in K} b_k e^{ik(x - ct)}
+ \half \sum_{k\in K} b_k e^{ik(x + ct)}
Our interest: one component e^{i(kx -\omega t)} , \omega = kc
