$A$ transverse wave is described by the equation $Y = Y_0 \sin 2\pi \left( ft - \frac{x}{\lambda} \right)$. The maximum particle velocity is four times the wave velocity if:

The figure represents the instantaneous snapshot of a transverse harmonic wave traveling along the negative $x$-axis. Choose the correct alternative(s) related to the movement of the points shown in the figure. The point(s) moving downwards is/are:

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

$A$ wave is propagating along the $x$-axis. The displacement of particles of the medium in the $z$-direction at $t = 0$ is given by: $z = \exp[-(x + 2)^2]$,where $x$ is in meters. At $t = 1 \ s$,the same wave disturbance is given by: $z = \exp[-(2 - x)^2]$. Then,the wave propagation velocity is:

The displacement of a particle in a medium is $y = 10^{-4} \sin(100t + 20x + \frac{\pi}{3}) \ m$,where $t$ is in seconds and $x$ is in metres. The speed of the wave is (in $m/s$)

$A$ simple wave motion is represented by $y=5(\sin 4 \pi t+\sqrt{3} \cos 4 \pi t)$. Its amplitude is