$y(x,t)=\frac{0.8}{\left[(4x+5t{)}^2+5\right]}$ represents a moving pulse where $x$ and $y$ are in metre and $t$ in second. Then, choose the correct alternative(s):

The shape of pulse at x=0 end t=0 would be

$y(0,0)=\frac{0.x}{6}=0.16 \mathrm{m}$

From the equation it is clear that$y_{max}=0.16 \mathrm{m}$

Pulse will be asymmetric (asymmetry is checked about$y_{max}$ if

$At t=0; y\left(x\right)=y(-x)$

From the given equation

$\left.\begin{array}{c}y\left(x\right)=\frac{0.8}{16x^2+5}\\ y(-x)=\frac{0.8}{16x^2+6}\end{array}\right\}att=0y\left(x\right)=y(-x)$

Therefore, pulse is symmetric.

Speed of pulse

At $t=1 \mathrm{s} and s=-1.25 \mathrm{m}$ value of y is again $0.16 \mathrm{m},$i.e. pulse has travelled a distance of $1.25 \mathrm{m}$ in one second in negative x-direction or we can say that the speed of pulse is $1.25 \mathrm{m}/\mathrm{s}$ and it is travelling in negative x-direction. Therefore, it will travel a distance of $2.5 \mathrm{m}$ in two seconds..