An observer standing near the sea shore observes $54$ waves per minute. If the wavelength of the water wave is $10 \ m$,then the velocity of the water wave is .... $m/s$.

$A$ wave travelling in the $-z$ direction having displacement along the $x$ direction as $1 \ m$,wavelength $\pi \ m$,and frequency $\frac{1}{\pi} \ Hz$ is represented by:

$A$ sound wave of frequency $500 \text{ Hz}$ travels between two points $X$ and $Y$ separated by a distance of $600 \text{ m}$ in a time of $2 \text{ s}$. The number of waves between the points $X$ and $Y$ are

$Assertion :$ Speed of wave $= \frac{\text{wavelength}}{\text{time period}}$
$Reason :$ Wavelength is the distance between two nearest particles in phase.

Write the definition of the angular frequency of a wave and its $SI$ unit.

$A$ wave motion has the function $y = a_0 \sin(\omega t - kx)$. The graph in the figure shows how the displacement $y$ at a fixed point varies with time $t$. Which one of the labelled points shows a displacement equal to that at the position $x = \frac{\pi}{2k}$ at time $t = 0$?