When a wave travels in a medium,the particle displacement is given by $y = a \sin(2 \pi (bt - cx))$,where $a, b$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity if

$A$ 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 progressive wave is $y = 4 \sin(4 \pi t - 0.04 x + \pi / 3)$, where $x$ is in meters and $t$ is in seconds. The velocity of the wave is:

In a plane progressive wave given by $y = 25 \cos (2\pi t - \pi x)$,the amplitude and frequency are respectively

$A$ travelling wave passes a point of observation. At this point,the time interval between successive crests is $0.2 \ s$. Which of the following is true?

$A$ simple harmonic progressive wave is given by $Y = Y_0 \sin 2 \pi (nt - \frac{x}{\lambda})$. If the wave velocity is $(1/8)^{\text{th}}$ of the maximum particle velocity,then the wavelength is