Question

$Y(x,t)=\frac{0.8}{[(4x+5t{)}^2+5]}$ represents a moving pulse where $x$ and $y$ are in metre and $t$ is in second. Then

• A. pulse 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 symmetric pulse

Answer 1

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

The shape of pulse at $x=0$ and $t-0$ would be as shown, in Fig. (a).
$y(0,0)=\frac{0.8}{5}=0.16m$
From the figure it is clear that $y_{max}=0.16m$
Pulse will be symmetric (Symmetry is checked about
$y_{max})$ if at $t=0y(x)=y(-x)$
From the given equation,

Therefore, pulse is symmetric. Speed of pulse
At $t=1s$ and $x=-1.25m$ value of $y$ is again $0.16m$,
i.e. pulse has travelled a distance of $1.25m$ in $1s$ in negative $x$-direction or we can say that the speed of pulse is $1.25m/s$ and it is travelling in negative $x$-direction.
Therefore, it will travel a distance of $2.5m$ in $2s$.
The above statement can be better understood from Fig. (b).