A wave pulse is travelling on a string at `2m//s` along positive x-directrion. Displacement y of the particle at x = 0 at any time t is given by
`y = (2)/(t^(2) + 1)` Find
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 = 1 s 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 is equal to wave speed. Here is the procedure.
`y = (2)/((t - (x)/(2))^(2)+1)at 1 = 1s`
`{:(at," "x = 2 ," "y = 2 "(maximum value)"),(at," "x = 0 ," "y = 1),(at," "x = 4," "y = 1):}`
The pulse has moved to the right by 2 units in 1st interval