$A$ transverse wave is described by the equation $Y = Y_0 \sin 2\pi \left( ft - \frac{x}{\lambda} \right)$. The maximum particle velocity is four times the wave velocity if:

The figure represents the instantaneous snapshot of a transverse harmonic wave traveling along the negative $x$-axis. Identify the correct point(s) moving in the negative $y$-direction (downward).

Write the equation of the relation between wave speed,wavelength,and time period.

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 transverse wave is given by $y=0.05 \sin \pi(2 t-0.02 x)$,where $x, y$ are in metre and $t$ is in second. The minimum distance of separation between two particles which are in phase and the wave velocity are respectively

The figure shows the shape of a part of a long string in which transverse waves are produced by attaching one end of the string to a tuning fork of frequency $250 \ Hz$. What is the velocity of the waves in $ms^{-1}$?