The distance between two consecutive points with a phase difference of $60^{\circ}$ in a wave of frequency $500\,Hz$ is $6.0\,m$. The velocity with which the wave is traveling is $.........\,km/s$.

$A$ transverse wave in a medium is given by $y = A \sin 2(\omega t - kx)$. It is found that the magnitude of the maximum velocity of particles in the medium is equal to the magnitude of the wave velocity. What is the value of $A$?

The path difference between two waves given by the equations $y_1 = a_1 \sin \left(\omega t - \frac{2 \pi x}{\lambda}\right)$ and $y_2 = a_2 \sin \left(\omega t - \frac{2 \pi x}{\lambda} + \phi\right)$ is

The disturbance $y(x, t)$ of a wave propagating in the positive $x$-direction is given by $y = \frac{1}{1 + x^2}$ at time $t = 0$ and by $y = \frac{1}{1 + (x - 1)^2}$ at $t = 2 \ s$,where $x$ and $y$ are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of the wave in $m/s$ is:

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.

$A$ travelling wave is described by the equation $y(x, t) = 0.05 \sin(8x - 4t) \; m$. The velocity of the wave is $..... \; m/s$ [all the quantities are in $SI$ units].