The displacement due to a wave moving in the positive $x$-direction is given by $y = \frac{1}{(1 + x^2)}$ at time $t = 0$ and by $y = \frac{1}{[1 + (x - 1)^2]}$ at $t = 2$ seconds,where $x$ and $y$ are in metres. The velocity of the wave in $m/s$ is

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

$A$ simple harmonic progressive wave is represented by the equation $y = 8\sin 2\pi (0.1x - 2t)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. At any instant,the phase difference between two particles separated by $2.0 \, cm$ in the $x$-direction is ..... $^o$.

Define wavelength and state its $SI$ unit.

$A$ progressive sound wave is represented by $y = a \sin(400\pi t - \pi x / 6.85)$,where $x$ is in $m$ and $t$ is in $s$. The frequency of the wave is .... $Hz$.

$A$ sound wave of frequency $245 \,Hz$ travels with the speed of $300 \,ms^{-1}$ along the positive $x$-axis. Each point of the wave moves to and fro through a total distance of $6 \,cm$. What will be the mathematical expression of this travelling wave?