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 .... $m/s$.

$A$ sound wave of frequency $210 \text{ Hz}$ travels with a speed of $330 \text{ ms}^{-1}$ along the positive $x$-axis. Each particle of the wave moves a distance of $10 \text{ cm}$ between the two extreme points. The equation of the displacement function $s(x, t)$ of this wave is ($x$ in metre, $t$ in second):

$A$ wave is given by $y=5 \times 10^{-3} \sin \left(12.5 \pi x - \frac{\pi}{2} t\right)$. Then its wavelength and time period are respectively ($y$ and $x$ are in metres and $t$ is in seconds).

The equation of a sound wave is $y = 0.0015 \sin (62.4x + 316t)$. The wavelength of this wave is ..... $unit$.

$A$ wave travelling along the $x$-axis is described by the equation $y(x, t) = 0.005 \cos(\alpha x - \beta t)$. If the wavelength and the time period of the wave are $0.08 \ m$ and $2.0 \ s$,respectively,then $\alpha$ and $\beta$ in appropriate units are:

If a given wave has a propagation constant of $\frac{5 \pi}{7} \, rad/m$,then the phase difference between two particles having a distance difference of $\frac{49}{22} \, m$ is ..... $rad.$ (Take $\pi = \frac{22}{7}$)