Question

The shape of the pulse at t = 0 and t = 1s

Answer 1

We can use wave function at a particular instant say t = 0 to find shape of the wave pulse using different values of x
at t = 0 $y=\frac{2}{\frac{x^2}{4}+1}$
at x = 0 y = 2
x = 2 y = 1
x = -2 y = 1
x = 4 y = 0.4
x = -4 y = 0.4
Using these value shape is drawn Similarly for t = 1s shape can be drawn What do you conclude about direction of motion of the wave from the graphs ? Also check how much the pulse has moved in 1s time interval This equal to wave speed Here is the procedure $y=\frac{2}{{(1-\frac{x}{2})}^2+1}$
at t = 1s
at t = 2 y = 2 (maximum value)
at t = 0 y = 1
at t = 4 y = 1
The pulse has moved to the right by 2 units in 1s interval
Also as $t-\frac{x}{2}$
Differentiating w.r.t. time
$1-\frac{1}{2}.\frac{dx}{dt}=0$ $\Rightarrow$ $\frac{dx}{dt}=2$