Question

$Y(x,t)=\frac{0.05}{\left[\right(4x+2t{)}^2+5]}$ represents a moving wave pulse, where $x$ and $y$ are in meters and $t$ is in seconds. Then which statement(s) are correct :

• A. pluse is moving in $-x$ direction
• B. wave speed is $0.5m/s$
• C. max. particle displacement is $1cm$
• D. it is a symmetric pulse

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A pluse is moving in $-x$ direction
B wave speed is $0.5m/s$
C max. particle displacement is $1cm$
D it is a symmetric pulse

Given:
$Y(x,t)=\frac{0.05}{(4x+2t{)}^2+5}$
The general equation for a wave is given by $f(\omega t-kx)=Y(x,t)$;
Comparing with the given equation we get $\omega =2rad{s}^{-1}$
and $k=-4m^{-1}$
$v=\frac{\omega }{k}$
$v=-0.5m{s}^{-1}$ (negative sign indicates travel in negative x direction)
The function obtains maximum displacement when $(4x+2t)$ vanishes $(=0)$
At this point the displacement is $\frac{0.05}{5}=0.01m=1cm$
We can also see that
$Y(\delta -\frac{t}{2},t)=Y(-\delta -\frac{t}{2},t)$
What this implies is that the function Y(x,t) is symmetric about $x=-\frac{t}{2}$
Hence the pulse is symmetric.