Two travelling waves produce a standing wave represented by the equation,
${y} = 1.0 \, \text{mm} \cos(1.57 \, \text{cm}^{-1} x) \sin(78.5 \, \text{s}^{-1} t)$
The node closest to the origin in the region ${x} > 0$ will be at ${x} = \dots \, \text{cm}$.

The expression $y = a \sin bx \sin \omega t$ represents a stationary wave. The distance between the consecutive nodes is equal to

If in a stationary wave the amplitude corresponding to an antinode is $4 \,cm$,then the amplitude corresponding to a particle of medium located exactly midway between a node and an antinode is ........... $cm$.

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

Spacing between two successive nodes in a standing wave on a string is $x$. If the frequency of the standing wave is kept unchanged but the tension in the string is doubled,then the new spacing between successive nodes will become

$A$ standing wave having $3$ nodes and $2$ antinodes is formed between two atoms having a distance of $1.21 \; \mathring{A}$ between them. The wavelength of the standing wave is .... $\mathring{A}$