The number of waves counted by an observer on the sea-coast in one minute is $54$. If the wavelength of the waves is $5 \text{ m}$, then the velocity of the waves in $\text{m/s}$ will be:

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 .... $Hz$.

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 $Hz$)

$A$ wave is represented by the equation: $y = a \sin(0.01x - 2t)$,where $a$ and $x$ are in $cm$. The velocity of propagation of the wave is .... $cm/s$.

$A$ 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 $t = 20 \, s$.

The equation of a wave is given by $Y = 7 \sin(7\pi t - 0.04\pi x + \frac{\pi}{3})$. What is the wave speed in $m/s$?