`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 +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 symmetric pulse

Answer

B, C, D

Explanation

Given `y=(0.8)/((4x+5t)^(2))=(0.8)/(16[x+(5)/5t]^(2)+5)`….(i)
We know that equation of moving pulse is
y=f(x+t)…..(ii)
on comparing Eqs (i) and (ii), we get
`v=5/4m//s=(2.5)/2m//s`
wave will travel a distance of 2.5m in 2s.
y is maximum when `(16(x+(5t)/4)^(2)+5)`is minimum
which is when `x+(5t)/4=0toy_(max)=(0.8)/5=0.16m`