`y(x, t) =(0.8)/([(4x + 5t)^(2) +5])` represents a moving pulse where `x` and `y` are in metre and `t` in second. Then,choose the correct alternative(s):
(a) pules is moving in positive x- direction
(b) in `2 s` it will travel a distance of `2.5 m`
(c) its maximum displacement is `0.16 m`
(d) it is a sysmmetric pulse

Explanation

`(b), (c)` and `(d)` are correct option. ,

`t=0`
The shape of pulse at `x-0` and `t=0` would be as shown in figure
`y(0, 0)=(0.8)/(5)=0.16 m`
From the equation it is clear that `y_(max) = 0.16 m`
Pulse will be symmetric (symmetry is checked about `y_(max)) if
At `t=0` , `y(x) = y(-x)`
From the given equation
`y(x)=(0.8)/(16x^2+5)`
and `y(-x)=(0.8)/(16x^2+5) } at t=0`
or `y(x)=y(-x)` Therefore, pulse is symmetric.
Speed of pulse

At `t =1s` and `x=1.25 m`, value of `y` is again `0.16 m`, i.e. pulse has travelled a distance of `1.25m` in `1` second in negative x- direction or we can say that the speed of pulse is `1.25m//s` and it is travelling in x-direction. Therefore, it will travel a distance of `2.5 m` in `2 seconds`.