`y(x, t) = 0.8//[4x + 5t)^(2) + 5]` represents a moving pulse, where `x` and `y` are in meter and `t` in second. Then

Options

A. (a) pulse is moving in + x direction
B. (b) in `2 s` it will travel a distance of `2.5m`
C. ( c ) its maximum displacement is `0.16m`
D. (d) it is a sysmmetric pulse

Answer

B, C, D

Explanation

(b,c,d ) `y = (0.8)/((4x + 5t)^(2) + 5) = (0.8)/(16[x + (5)/(4)t]^(2) + 5` …(i)
We know that equation of moving pulse is
`y = f(x + vt)`
On comparing `(1) and (2)`, we get
`v = (5)/(4)ms^(-1) = (2.5)/(2)ms^(-1)`
So, the wave will travel a distance of `2.5m` in `2sec`.
`because` `y = (0.8)/((4x + 5t)^(2) + 5)`
At
`x = 0`, `y = (0.8)/(5) = 0.16m`
:. maximum displacement is `0.16m`
The graph for the given equation is drawn. This is sysmmetric about `y-axis`.