The transverse displacement of a string (clamped at its both ends) is given by $y(x,t) = 0.06 \sin(2\pi x / 3) \cos(120\pi t)$. All the points on the string between two consecutive nodes vibrate with

$A$ wave of frequency $100 \, Hz$ is sent along a string towards a fixed end. When this wave travels back after reflection,a node is formed at a distance of $10 \, cm$ from the fixed end of the string. The speed of the incident (and reflected) wave is .... $m/s$.

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

The standing wave in a medium is expressed as $y = 0.2 \sin(0.8 x) \cos(3000 t) \, m$. The distance between any two consecutive points of minimum or maximum displacement is

Two waves of same frequency $(n)$ approaching each other with same velocity of $18\text{ m/s}$ interfere. The distance between two consecutive antinodes is

$A$ standing wave having $3$ nodes and $2$ antinodes is formed between two atoms having a distance of $1.21 \ Å$ between them. The wavelength of the standing wave is (in $Å$)