$A$ boat at anchor is rocked by waves whose crests are $100 \,m$ apart and velocity is $25 \,m/s$. The boat bounces up once in every (in $\,s$)

$A$ wave is given by $y=5 \times 10^{-3} \sin \left(12.5 \pi x - \frac{\pi}{2} t\right)$. Then its wavelength and time period are respectively ($y$ and $x$ are in metres and $t$ is in seconds).

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 figure shows the wave $y = A \sin(\omega t - kx)$. What is the magnitude of the slope of the curve at $B$?

$A$ 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.

In the given progressive wave equation,what is the maximum velocity of the particle? $Y = 0.5 \sin(10\pi t - 5x) \text{ cm}$