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 .... $cm$.

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.

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 $\text{ km/s}$)

$A$ plane wave is described by the equation $y = 3 \cos \left( \frac{x}{4} - 10t - \frac{\pi}{2} \right)$. The maximum velocity of the particles of the medium due to this wave is

The figure represents the instantaneous snapshot of a transverse harmonic wave traveling along the negative $x$-axis. Identify the correct point(s) moving in the negative $y$-direction (downward).

Two sound waves having a phase difference of $60^{\circ}$ have a path difference of