The equation of a transverse wave in a stretched string is $y = 5 \sin 2\pi \left[ \frac{t}{0.04} - \frac{x}{50} \right]$,where distances are in $cm$ and time is in seconds. The wavelength of the wave is .... $cm$.

If a given wave has a propagation constant of $\frac{5 \pi}{7} \, rad/m$,then the phase difference between two particles having a distance difference of $\frac{49}{22} \, m$ is ..... $rad.$ (Take $\pi = \frac{22}{7}$)

The figure represents the instantaneous picture of a transverse harmonic wave traveling along the negative $x$-axis. Choose the correct alternative$(s)$ related to the movement of the nine points shown in the figure. The points moving upward is/are

Write the definition of the time period of a wave.

The equation of a progressive wave is $y = a \sin \left( \frac{\pi}{2}x - 200\pi t \right)$. The frequency of the wave will be .... $Hz$.

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: