$A$ progressive wave travelling along the positive $x-$ direction is represented by $y(x, t) = A \sin(kx - \omega t + \phi)$. Its snapshot at $t = 0$ is given in the figure. For this wave,the phase $\phi$ is

The equation for a spherical progressive wave is (where $r$ is the distance from the source):

The amplitude of a wave disturbance propagating in the positive $X-$ direction is given by $y = 1/(1 + x^2)$ at time $t = 0$ and by $y = 1/[1 + (x - 1)^2]$ at $t = 2$ seconds,where $x$ and $y$ are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is ..... $ms^{-1}$.

$A$ travelling wave is described by the equation $y(x, t) = 0.05 \sin(8x - 4t) \; m$. The velocity of the wave is $..... \; m/s$ [all the quantities are in $SI$ units].

Define wave speed.

The displacement $y$ of a wave travelling in the $x$-direction is given by $y = 10^{-4} \sin(600t - 2x + \frac{\pi}{3}) \, \text{m}$,where $x$ is expressed in metres and $t$ in seconds. The speed of the wave in $\text{m/s}$ is: