A wave pulse is travelling along +x direction on a string at `2 m//s`. Displacement y (in cm ) of the parrticle at x=0 at any time t is given by `2//(t^(2)+1)`. Find
(i) expression of the function y=(x,t),i.e., displacement of a particle at position x and time t.
Draw the shape of the pulse at t=0 and t=1 s.

Explanation

(i) By replacing t by `t-(x//v)`, we can get the desire wave function, i.e.,
`y=2/((t-x/2)^(2)+1)` (ii) we can use wave function at a particular instant to find the shape of the wave pulse using different values of `x`.
at `t=0, y=2/((x^(2))/(4)+1)`
at `x=0, y=2 cm`
`x=2 cm, y=1 cm`
`x=-2 cm, y=1 cm`
`x=4 cm, y=0.4 cm`
`x=-4 cm, y=0.4 cm`
using these value, shape of the pulse is drawn.
similarly for `f=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 has moved in `1 s` time interval. this is equal to wave speed. here is the procedure:
at `t=1 s. y=2/((1-x/2)^(2)+1)`
at `x=2m y=2 cm` (maximum value)
at `x=0 y=1 m`
at `x=4 m y=1 cm`
The pulse has moved to the right by `2` in `1 s` interval.