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 $\pi = \frac{22}{7}$)

$A$ travelling wave pulse is given by $y = \frac{4}{3x^2 + 48t^2 + 24xt + 2}$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The velocity of the wave is ........... $m/s$.

$A$ plane progressive wave is given by $y = 2 \cos 2 \pi (330 t - x) \ m$. The frequency of the wave is: (in $Hz$)

$A$ longitudinal wave is represented by $x = 10 \sin 2 \pi (nt - \frac{x}{\lambda}) \, cm$. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to .....................

$A$ transverse wave in a medium is described by the equation $y = A \sin^2 (\omega t - kx)$. The magnitude of the maximum velocity of particles in the medium will be equal to that of the wave velocity,if the value of $A$ is ($\lambda$ = wavelength of wave).

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