A wave pulse is travelling on a string at 2 m/s. displacement y of the particle at x = 0 at any time t is given by
`y=2/(t^2+1)`
Find
(ii) Shape of the pulse at t = 0 and t = 1s.

Explanation

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=2/((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 drawn. What do you conclude about direction of motion of the wave from the graphs? Also check how much the pulse has move in 1s time interval. This is equal to wave speed. Here is the procedure.
Also as `t-x/2` = constt.
Differentiating w.r.t. time
`1-1/2*(dx)/(dt)=0 rArr (dx)/(dt)=2`