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## Homework Statement

Graph snapshots of the solution in the

*x-u*plane for various times

*t*if

\begin{align*}

f(x) =

\begin{cases}

& 3, \text{if } -4 \leq x \leq 0 \\

& 2, \text{if } 4 \leq x \leq 8 \\

& 0, \text{otherwise}

\end{cases}

\end{align*}

## Homework Equations

Assuming that c=1 and g(x) = 0, D'Alembert's solution for this question is $$f(x) = \frac{1}{2} \left(f(x+ct) - f(x-ct)\right)$$

## The Attempt at a Solution

I'm struggling with this problem in its entirety. I don't understand how to graph the solution and why it's a rectangular box that is basically reversal of what seems to make sense when plugging in various values for x based off of the equation's characteristics. Conceptually, I realize that it is an infinite string and there's shifting of two waves that will overlap for some points. What I don't understand is how to go about drawing these graphs by hand. I confirmed with a classmate that the 'endpoints' for t are t = 2, t = 4, t = 4, and t = 6, based on the fact that t = distance/velocity.

Please explain this to me like I'm 5. I tried Googling the concept to death and came short, and my professor and the textbook aren't particularly helpful. Any guidance would be very much appreciated.