The equation of a progressive wave is given by $y = a \sin(628t - 31.4x)$. If the distances are expressed in $cm$ and time in seconds,then the wave velocity will be ...... $cm/sec$.

Write the definition of the speed of a progressive wave and derive $v = \frac{\omega}{k}$ and $v = \frac{\lambda}{T}$.

Given below are some functions of $x$ and $t$ to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent a travelling wave.

The equation of a progressive wave is given by $y = 0.2 \cos \pi (0.04t + 0.02x - \frac{\pi}{6})$. The distance is expressed in $cm$ and time in seconds. What will be the minimum distance between two particles having a phase difference of $\pi / 2$ in $cm$?

For a progressive wave given by the equation $y = 4 \sin \frac{\pi}{2} (8t - \frac{x}{8}) \, cm$,what is the wave velocity and its direction?

$A$ progressive wave of frequency $50\text{ Hz}$ is travelling with velocity $350\text{ m/s}$ through a medium. The change in phase at a given time interval of $0.01\text{ s}$ is