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

The stationary wave $y = 2a{\mkern 1mu} \,\,sin\,\,{\mkern 1mu} kx{\mkern 1mu} \,\,cos{\mkern 1mu} \,\omega t$ in a stretched string is the result of superposition of $y_1 = a\,sin\,(kx -\omega t)$ and

A man fires a bullet standing between two cliffs. First echo is heard after $3\, seconds$ and second echo is heard after $5\, seconds$. If the velocity of sound is $330\,m/s$, then the distance between the cliffs is .... $m$

Waves of displacement amplitude $A$ and angular frequency $\omega $ travel in air with the same velocity. Which of the following waves has the highest intensity

A closed organ pipe has a frequency $'n'$. If its length is doubled and radius is halved, its frequency nearly becomes

Three waves of equal frequency having amplitudes $10\,\mu m$, $4\,\mu m$, $7\,\mu m$ arrive at a given point with successive phase difference of $\pi /2$, the amplitude the resulting wave in $\mu m$ is given by