In the wave equation $y = 0.5 \sin \frac{2 \pi}{\lambda}(400 t - x ) \, m$,the velocity of the wave will be ......... $m/s$.

The phase difference between the following two waves $y_1$ and $y_2$ is:
$y_1 = a \sin(\omega t - kx)$
$y_2 = b \cos(\omega t - kx + \frac{\pi}{3})$

In a plane progressive wave given by $y = 25 \cos (2\pi t - \pi x)$,the amplitude and frequency are respectively

The figure represents the instantaneous picture of a transverse harmonic wave travelling along the negative $x$-axis. Identify the correct statement(s) related to the movement of the points shown in the figure. The points moving opposite to the direction of propagation (i.e., moving in the negative $y$-direction) are:

$A$ wave travels uniformly in all directions from a point source in an isotropic medium. The displacement of the medium at any point at a distance $r$ from the source may be represented by ($A$ is a constant representing strength of source)

The equation of wave motion is $Y = 6 \sin (12\pi t - 0.02\pi x + \pi/3)$ where $x$ is in metre and time in second. The velocity of the wave is (in $\text{ m/s}$)