$A$ transverse wave is represented by the equation $y=2 \sin (30 t-40 x)$ where the measurements of distances are in meters,then the velocity of propagation is (in $ms^{-1}$)

The maximum particle velocity in a wave motion is half the wave velocity. Then the amplitude of the wave is equal to

The equation of a travelling wave is $y = a \sin 2 \pi (p t - \frac{x}{5})$. Then the ratio of the maximum particle velocity to the wave velocity is ...........

For a wave equation $y = 8 \sin 2\pi (0.1x - 2t) \, cm$,find the phase difference in $^\circ$ between two particles separated by a distance of $2 \, cm$.

If a travelling wave is given by $y(x, t) = 0.5 \sin (70.1 x - 10 \pi t)$,where $x$ and $y$ are in metre,the time $t$ is in second,then the frequency of the wave is (in $Hz$)

$A$ person is producing a wave in a string by moving his hand first up and then down. If the frequency is $\frac{1}{8} \, Hz$,then find out the time taken by a particle which is at a distance of $9 \, m$ from the source to move to the lower extreme for the first time in seconds. (Given $\lambda = 24 \, m$)