The amplitude of a wave disturbance propagating in the positive $x$-direction is given by $y = \frac{1}{1+x^2}$ at time $t=0$ and $y = \frac{1}{1+(x-2)^2}$ at $t=1 \text{ s}$,where $x$ and $y$ are in meters. The shape of the wave does not change during the propagation. The velocity of the wave will be $... \text{ m/s}$.

The phase difference between two points separated by $0.8 \ m$ in a wave of frequency $120 \ Hz$ is $\frac{\pi}{2}$. The velocity of the wave is ..... $m/s$.

In a wave motion $y = a \sin (kx - \omega t)$,$y$ can represent

$A$ 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?

The path difference between two waves $Y_1 = a_1 \sin \left(\omega t - \frac{2 \pi x}{\lambda}\right)$ and $Y_2 = a_2 \cos \left(\omega t - \frac{2 \pi x}{\lambda} + \phi\right)$ is

State whether the following statements are True or False:
$(i)$ In the case of propagation of longitudinal waves,the angle between the directions of particle velocity and wave velocity is $0^{\circ}$ or $180^{\circ}$.
$(ii)$ In the case of propagation of transverse waves,the angle between the directions of particle velocity and wave velocity is $\pi \text{ rad}$.
$(iii)$ Along the direction of propagation of a wave,the distance between two particles having the same phase is called the wavelength of the wave.
$(iv)$ When a wave is reflected from a rarer medium,its phase increases by an amount of $\pi \text{ rad}$.