The distance between two consecutive points with a phase difference of $60^{\circ}$ in a wave of frequency $500 \text{ Hz}$ is $0.6 \text{ m}$. The velocity with which the wave is travelling is: (in $\text{ km/s}$)

$A$ 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:

The equation of a simple harmonic wave is given as $y = 5 \sin \frac{\pi}{2}(100t - x)$,where $x$ and $y$ are in meters and time $t$ is in seconds. The period of the wave is: (in $s$)

If the wave equation is $y = 0.08 \sin \frac{2\pi}{\lambda} (200t - x)$,then the velocity of the wave will be:

The diagram below shows the propagation of a wave. Which points are in the same phase?

The equation of a plane progressive wave is given by $y = 0.025 \sin (100t + 0.25x)$. The frequency of this wave would be