Answer
See the detailed answer below.
Work Step by Step
$$\bf a)$$ The given function represents a pulse with a constant shape that moves to the right.
$$ D_{(x,t)}=\begin{cases}
1\rm \;cm& \text{ if } |x-3t|\leq 1 \\
0\rm \;cm& \text{ if } |x-3t|\gt 1
\end{cases}$$
Noting that,
At $t=0\rightarrow $, $(-1\leq x\leq 1)$
At $t=1\rightarrow $, $(2\leq x\leq 4)$
At $t=2\rightarrow $, $(5\leq x\leq 7)$
At $t=3\rightarrow $, $(8\leq x\leq 10)$
See the graphs below.
$$\bf b)$$
To find the wave speed, we can watch the leading edge of it.
It is obvious that the leading edge is moving 3 meters each second.
$$v=\color{red}{\bf 3}\;\rm m/s$$
$$\bf c)$$
We need to find the speed of the wave, from the given function,
$$|x-3t|=D(x-vt)$$
Thus,
$$v=3\;\rm m/s$$
Hence, yes, it agrees with part b.
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