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
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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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