Question

$y(x,t)=0.8/\left[\right(4x+5t{)}^2+5]$ represents a moving pulse, where $x$ and $y$ are in metres and $t$ is in seconds, then

• A. pulse is moving in $+x$ direction
• B. in $2\text{s}$ it will travel a distance of $2.5\text{m}$
• C. its maximum displacement along y-axis is $0.16\text{m}$
• D. it is a symmetric pulse

Answer 1

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

it is a symmetric pulse

$y(x,t)=\frac{0.8}{16[{(x+\frac{5}{4}t)}^2+\frac{5}{16}]}$
$y(x,t)=\frac{0.05}{{(x+\frac{5}{4}t)}^2+\frac{5}{16}}$
where wave velocity $=5/4\text{m/s}$
Distance travelled by the wave with this velocity in $2\text{s}$ is
$\frac{5}{4}\times 2=2.5\text{m}$
$y(x,t)$ will be maximum when $4x+5t=0$
$y_{\text{max}}=\frac{0.8}{5}=0.16\text{m}$