# Square Pulse Train Fourier Series help?

Square Pulse Train Fourier Series help??

## Homework Statement

problem+directions below: ## Homework Equations

ω=2$\pi$f
β=$\frac{2\pi}{\lambda}$

## The Attempt at a Solution

Since the problem asks to make all time-dependent sinusoidal functions deal with x-direction, i don't think i need to worry about the sin function because it is dependent on td (duty cycle) and not time. I am aware of the cos format for x and t dependent but this is how i would plan to change it (for the equation with both sin and cos):
cos(n*2$\pi$f*t) -> cos[n(ωt-βx)]

basically I just factored out the n, and I don't think I need to include any phase shift. I just changed the cos part, the rest of the equation stays the same.

I can worry about using Fourier series with MATLAB later, I just wanted to know if the equation for the fourier series I had was right. also, I don't know how to find the value of wavelength for β, since it is not given anywhere. would i need to use the equation for phase velocity, if it is related to the f given somehow?

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1+$\frac{20}{\pi} \sum{\frac{1}{n}sin(\frac{n\pi}{10})cos[n(ωt-βx)]}$ where ω=2$\pi$*106, β=$\frac{2\pi}{300} = \frac{\pi}{150}$, and the fourier series goes from n=1 to a finite number N=1000 (not infinity).