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 .... $m/s$.

Give the definition,$SI$ unit,and dimensional formula of the time period,angular frequency,and frequency of a wave.

Give the definition,equation,and unit for wavelength and wave number for a wave.

The equation of a progressive wave is $y = a \sin \left( \frac{\pi}{2}x - 200\pi t \right)$. The frequency of the wave will be .... $Hz$.

Obtain the relation between wave velocity,angular frequency,and angular wave number.

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