The phase difference between two points separated by $0.8 \ m$ in a wave of frequency $120 \ Hz$ is $\frac{\pi}{2}$. The velocity of the wave is ..... $m/s$.

What is the phase difference between two successive crests in a wave?

$A$ 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 $\lambda = 24 \, m$)

The equation of a travelling wave is $y = 60 \cos (1800t - 6x)$,where $y$ is in microns,$t$ is in seconds,and $x$ is in metres. The ratio of maximum particle velocity to the velocity of wave propagation is:

If $\vec{u}$ is the instantaneous velocity of a particle and $\vec{v}$ is the velocity of the wave,then:

$A$ wave travelling along a string is described by,
$y(x, t) = 0.005 \sin (80.0 x - 3.0 t)$
In which the numerical constants are in $SI$ units ($0.005 \, m, 80.0 \, rad \, m^{-1},$ and $3.0 \, rad \, s^{-1}$). Calculate
$(a)$ the amplitude,
$(b)$ the wavelength,and
$(c)$ the period and frequency of the wave.
Also,calculate the displacement $y$ of the wave at a distance $x = 30.0 \, cm$ and time $t = 20 \, s$.