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 $\pi \text{ rad}$.

(A) $(i)$ True. In longitudinal waves,particles oscillate parallel or antiparallel to the direction of wave propagation,so the angle is $0^{\circ}$ or $180^{\circ}$.
$(ii)$ False. In transverse waves,particles oscillate perpendicular to the direction of wave propagation,so the angle is $\frac{\pi}{2} \text{ rad}$ $(90^{\circ})$.
$(iii)$ False. The distance between two consecutive particles having the same phase is called the wavelength. If the phase difference is not specified as $2\pi \text{ rad}$,the statement is incomplete.
$(iv)$ False. When a wave is reflected from a denser medium,its phase increases by $\pi \text{ rad}$. Reflection from a rarer medium involves no phase change.