A string of mass $M$ and length $L$ hangs freely from a fixed point. The velocity of transverse wave along the string at a distance $'x'$ from the free end will be

A pulse shown here is reflected from the rigid wall $A$ and then from free end $B.$ The shape of the string after these $2$ reflection will be

The speed of sound in oxygen $(O_2)$ at a certain temperature is $460\, ms^{-1}$. The speed of sound in helium $(He)$ at the same temperature will be ............. $\mathrm{m/s}$  (assume both gases to be ideal)

Which of the following is correct ?

The displacement $y$ of a wave travelling in the $x-$ direction is given by $y = {10^{ - 4}}\sin \left( {600t - 2x+\frac{\pi }{3}} \right)$ metre, where $x$ is expressed in metres and $t$ in seconds. The speed of the wave in $ms^{-1}$, is

A transverse harmonic wave on a string is described by $y = 3\sin \left( {36t + 0.018x + \frac{\pi }{4}} \right)$ where $x$ and $y$ are in $cm$ and $t$ in $s$. The least distance between two successive crests in the wave is .... $m$