$A$ transverse wave is travelling along a string from left to right. The adjoining figure represents the shape of the string at a given instant. At this instant,among the following,choose the wrong statement.

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 $\pi \text{ rad}$.

The equation of a wave is $Y = 6 \sin(12 \pi t - 0.02 \pi x + \frac{\pi}{3})$,where $x$ is in $m$ and $t$ is in $s$. The velocity of the wave is: (in $m/s$)

The speed of a wave in a medium is $760\, m/s$. If $3600$ waves are passing through a point in the medium in $2$ minutes, then its wavelength is ...... $m$.

$A$ wave travelling in the $+ve$ $x$-direction having displacement along $y$-direction as $1\, m$,wavelength $2\pi\, m$,and frequency of $\frac{1}{\pi}\ Hz$ is represented by

If the wave equation is $y = 0.08 \sin \frac{2\pi}{\lambda} (200t - x)$,then the velocity of the wave will be: