$A$ transverse wave in a medium is described by the equation $y = A \sin^2 (\omega t - kx)$. The magnitude of the maximum velocity of particles in the medium will be equal to that of the wave velocity,if the value of $A$ is ($\lambda$ = wavelength of wave).

$A$ wave is represented by the equation $y = 7\sin \{ \pi (2t - 2x) \} $ where $x$ is in metres and $t$ is in seconds. The velocity of the wave is ..... $m/s$.

Waves having a velocity $10 \text{ m/s}$ strike a stationary boat near the sea shore. The distance between two consecutive crests of the waves is $40 \text{ m}$. After how many seconds do the consecutive waves strike the boat (in $\text{ s}$)?

Consider the snapshot of a wave traveling in the positive $x$-direction.

One end of a long string of linear mass density $8.0 \times 10^{-3} \; kg \; m^{-1}$ is connected to an electrically driven tuning fork of frequency $256 \; Hz$. The other end passes over a pulley and is tied to a pan containing a mass of $90 \; kg$. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At $t=0$,the left end (fork end) of the string $x=0$ has zero transverse displacement $(y=0)$ and is moving along the positive $y$-direction. The amplitude of the wave is $5.0 \; cm$. Write down the transverse displacement $y$ as a function of $x$ and $t$ that describes the wave on the string.

If the speed of the wave shown in the figure is $330 \ m/s$ in the given medium,then the equation of the wave propagating in the positive $x$-direction will be (all quantities are in $M.K.S.$ units).