$A$ standing wave is represented by $Y = A \sin(100t) \cos(0.01x)$,where $Y$ and $A$ are in millimetres,$t$ is in seconds,and $x$ is in metres. The velocity of the wave is ..... $m/s$.

$A$ string is vibrating in its fifth overtone between two rigid supports $2.4 \ m$ apart. The distance between successive node and antinode is (in $m$)

In a stationary wave,all particles are

Standing stationary waves can be obtained in an air column even if the interfering waves are

Stationary waves are produced in a $10\,m$ long stretched string. If the string vibrates in $5$ segments and the wave velocity is $20\,m/s$,the frequency is ..... $Hz$.

The ends of a stretched wire of length $L$ are fixed at $x = 0$ and $x = L.$ In one experiment,the displacement of the wire is ${y_1} = A\sin (\pi x/L)\sin \omega t$ and energy is ${E_1}$,and in another experiment its displacement is ${y_2} = A\sin (2\pi x/L)\sin 2\omega t$ and energy is ${E_2}$. Then