A string of length $2L$, obeying Hooke's law, is stretched so that its extension is $L$. The speed of the transverse wave travelling on the string is $v$. If the string is further stretched so that the extension in the string becomes $4L.$ The speed of transverse wave travelling on the string will be

The graph shows a wave at $t=0$ travelling to the right with a velocity of $4 \mathrm{m}/\mathrm{s}$. The equation that best represents the wave is

The figure below is a representation of a simple harmonic progressive wave, progressing in the negative $X$-axis, at a given instant. The direction of the velocity of the particle at stage $P$ in the figure is best represented by the arrow.

A wave motion has the function $y=a_0\sin \left(\omega t-kx\right)$. The graph in figure shows how the displacement $y$ at a fixed point varies with time $t$. Which one of the labelled points shows a displacement equal to that at the position $x=\frac{\pi }{2k}$ at time $t=0$? 

For the wave shown in figure, write the equation of this wave if its position is shown at $t=0 .$ Speed of wave is $v=300 \mathrm{m}/\mathrm{s}$

A circular loop of rope of length $L$ rotates with uniform angular velocity $\mathrm{\omega }$ about an axis through its centre on a horizontal smooth platform. The velocity of pulse (with respect to rope) produced due to slight radial displacement is given by

A circular loop of rope of length $L$ rotates with uniform angular velocity $\mathrm{\omega }$ about an axis through its centre on a horizontal smooth platform. The velocity of pulse (with respect to rope) produced due to slight radial displacement is given by