$A$ wave represented by the equation $y = A \cos (kx - \omega t)$ is superimposed with another wave to form a stationary wave such that the point $x = 0$ is a node. The equation of the other wave is:

$A$ standing wave pattern of amplitude $A$ in a string of length $L$ shows $2$ nodes (plus those at two ends). If one end of the string corresponds to the origin and $v$ is the speed of the progressive wave,the disturbance in the string could be represented (with appropriate phase) as:

The equation of a stationary wave is $y = 0.8 \cos \left( \frac{\pi x}{20} \right) \sin (200 \pi t)$,where $x$ is in $cm$ and $t$ is in $sec$. The separation between consecutive nodes will be .... $cm$.

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

“Stationary waves” are so called because in them

$A$ string of mass $0.1 \ kg \ m^{-1}$ has length $0.9 \ m$. It is fixed at both ends and stretched such that it has a tension of $40 \ N$. The string vibrates in three segments with amplitude $0.3 \ cm$. The amplitude (maximum) of the particle velocity is (in $m/s$):