`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

Options

A. pulse is moving in positive x-direction
B. in 2 s it will travel a distance of 2.5 m
C. Its maximum displacment is 0.16 m
D. it is a symmetric pulse

Answer

B, C, D

Explanation

The shape of pulse at x = 0 and t = 0 would be as shown, in figure (a)
`y = (0,0) = (0.8)/(5) = 0.16 m`

from the figure it is clear that `y_(max) = 0.16 m`
Pulse will be symmetric (Symmetric is checked about `y_(max)`) if t = 0
y (x) = y(x)
From the given equation and
`{:(y(x)=(0.8)/(16x^(2)+5)),(y(-x)=(0.8)/(16x^(2)+5)):}}"at" t=0rArr y(x)=y(x)`
Therefore, pulse is symmetric
Speed of pulse
At t = 1s and x = 1.25 m

value of y is given 0.16 m, i.e. pulse has travelled a distance of 1.25 m in 1s negative x-direction or we can say that the speed of pulse is 1.25 m/s and it is travelling in negative x-direction. Therefore, it will travel a distance of 2.5 m in 2s.
The above statement can be better understood from figure (b).