The equation of a progressive wave is given by $y = a \sin \pi [\frac{t}{2} - \frac{x}{4}]$,where $t$ is in seconds and $x$ is in meters. The distance through which the wave moves in $8 \ s$ is .... $(m)$

The equation of a plane progressive wave is given by $y = 0.6 \sin 2\pi \left( t - \frac{x}{2} \right)$. On reflection from a denser medium,its amplitude becomes $2/3$ of the amplitude of the incident wave. The equation of the reflected wave is:

The equation of a progressive wave is $y = 0.02 \sin 2\pi \left[ \frac{t}{0.01} - \frac{x}{0.30} \right]$. Here $x$ and $y$ are in $m$ and $t$ is in $s$. The velocity of propagation of the wave is .... $ms^{-1}$.

$A$ progressive wave of frequency $400 \ Hz$ is travelling with velocity $336 \ m/s$. How far apart are the two points on a wave which are $60^{\circ}$ out of phase (in $m$)?

$A$ progressive wave moving along the $x$-axis is represented by $y = A \sin \left[ \frac{2 \pi}{\lambda} (vt - x) \right]$. The wavelength $\lambda$ at which the maximum particle velocity is $3$ times the wave velocity is:

The diagram below shows an instantaneous position of a string as a transverse progressive wave travels along it from left to right. Which one of the following correctly shows the direction of the velocity of the points $1, 2$ and $3$ on the string?