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## Homework Statement

The question is to sketch for values of t = 0, t =0.25, t = 1, t=1.25 and t = 1.5 for the wave equation

Ytt = Yxx in the semi-infinite domain with initial conditions

y(x,0) = f(x) =

\begin{cases}

1 & \text{if } 0≤x≤1 \\

0 & otherwise

\end{cases}

Yt (x,0) = 0 and boundary condition of y(0,t) = 0

so I changed f(x) into D(x) where

D(x) =

\begin{cases}

1 & \text{if } 0≤x≤1 \\

-1 & \text{if } -1≤x≤0 \\

0 & otherwise

\end{cases}

## Homework Equations

Y(x,t) = Φa(x,t) +Φb(x,t)

where Φa(x,t) = 1/2 D(x+t)

and Φb(x,t) = 1/2 D(x-t)

## The Attempt at a Solution

These are the sketches. Can somebody please tell me if they are all correct for this question!