The displacement $y$ of a wave travelling in the $x$-direction is given by $y = 10^{-4} \sin(600t - 2x + \frac{\pi}{3}) \, \text{m}$,where $x$ is expressed in metres and $t$ in seconds. The speed of the wave in $\text{m/s}$ is:

An observer standing near the sea shore observes $54$ waves per minute. If the wavelength of the water wave is $10 \ m$,then the velocity of the water wave is .... $m/s$.

The figure represents the instantaneous picture of a longitudinal harmonic wave travelling along the negative $x$-axis. Identify the correct statement$(s)$ related to the movement of the points shown in the figure. The points with maximum displacement are:

The distance between two consecutive points with a phase difference of $60^{\circ}$ in a wave of frequency $500 \text{ Hz}$ is $0.6 \text{ m}$. The velocity with which the wave is travelling is: (in $\text{ km/s}$)

Write the definition of wave speed and derive $v = \frac{\omega}{k}$.

The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t) = e^{-(ax^2 + bt^2 + 2\sqrt{ab}xt)}$. This represents: