A common problem in wave optics involves the superposition of multiple coherent waves. Consider a ce

Question

A common problem in wave optics involves the superposition of multiple coherent waves. Consider a certain oscillation that results from the addition of $N$ coherent oscillations of the same direction, given by the equations $\xi_k = a \cos [\omega t + (k-1)\varphi]$, where $k = 1, 2, \dots, N$, and $\varphi$ is the constant phase difference between the $k$-th and $(k-1)$-th oscillations.

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