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## Homework Statement

Ytt = 1 Yxx

with initial conditions of

yT(x,0) = 0

y(x,0) = \begin{cases}

1 & \text{if } x \geq 0 \

& \text{if } x \leq 1 \\

0 & \text{if } otherwise

\end{cases}

Sketch the solution of this wave equation for 5 representative values of t, when the solution of the wave is considered on the infinite domain

## Homework Equations

D'alembert solution

## \frac {1} {2} \ ## (f(x+ct)+f(x-ct)) + ## \frac {1} {2c} \ ## ## \int_{x-ct}^{x+ct} g(x) \ ##

## The Attempt at a Solution

As the g(x) part was 0 I tried solving it by

y(x,t) = φ1(x,t) + φ2(x,t)

where φ1 = ## \frac {1} {2} \ ## f(x+ct) and φ2 = ## \frac {1} {2} \ ## f(x-ct)

but I am not sure how to sketch it, can somebody please help me?

The solution should look like this