A wave is propagating along x-axis. The displacement of particles… - Vidyadip

MCQ

A wave is propagating along $x$-axis. The displacement of particles of the medium in $z$-direction at $t = 0$ is given by: $z =$ exp$[ -(x + 2)^2]$ , where $‘x’$ is in meters. At $t = 1s$, the same wave disturbance is given by: $z =$ exp $ [ - (2 - x)^2 ]$. Then, the wave propagation velocity is

✓
$4 m/s$ in $+ x$ direction
B
$4 m/s$ in $-x$ direction
C
$2 m/s$ in $+ x$ direction
D
$2 m/s$ in $- x$ direction

✓

Answer

Correct option: A.

$4 m/s$ in $+ x$ direction

a
Let wave equation be

$z=e^{-\left|x-v\left(t-t_{0}\right)\right|^{2}}$

At $t=0, x+v t_{0}=x+2 \Rightarrow v t_{0}=2$

At $t=1 s, x-v\left(1-t_{0}\right)=x-2 \Rightarrow v=+4 m / s$

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