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(A) The general equation of a wave moving with velocity $v$ is given by $z(x, t) = f(x - vt)$.At $t = 0$,the wave is $z = \exp[-(x + 2)^2]$. This repr

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

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(A) The general equation of a wave moving with velocity $v$ is given by $z(x, t) = f(x - vt)$.At $t = 0$,the wave is $z = \exp[-(x + 2)^2]$. This represents a pulse centered at $x = -2$.At $t = 1 \ s$,the wave is $z = \exp[-(2 - x)^2] = \exp[-(x - 2)^2]$. This represents the same pulse now centered at $x = 2$.The pulse has moved from $x = -2$ to $x = 2$ in $1 \ s$.The displacement $\Delta x = 2 - (-2) = 4 \ m$.The time interval $\Delta t = 1 \ s$.The velocity $v = \frac{\Delta x}{\Delta t} = \frac{4 \ m}{1 \ s} = 4 \ m/s$.Since the pulse moved in the positive $x$-direction,the velocity is $4 \ m/s$ in the $+x$ direction.

$A$ wave is propagating along the $x$-axis. The displacement of particles of the medium in the $z$-direction at $t = 0$ is given by: $z = \exp[-(x + 2)^2]$,where $x$ is in meters. At $t = 1 \ s$,the same wave disturbance is given by: $z = \exp[-(2 - x)^2]$. Then,the wave propagation velocity is:

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