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

The stationary wave produced on a string is represented by the equation $y = 5 \cos (\pi x / 3) \sin (40 \pi t)$. Where $x$ and $y$ are in $cm$ and $t$ is in seconds. The distance between consecutive nodes is .... $cm$.

The equation $y = 0.15 \sin(5x) \cos(300t)$ describes a stationary wave. The wavelength of the stationary wave is .... $m$.

$A$ wave $y = a \sin(\omega t - kx)$ on a string meets with another wave producing a node at $x = 0$. Then the equation of the unknown wave is

$A$ 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 $m/s$):

The vibrations of a string of length $60 \, cm$ fixed at both ends are represented by the equation $y = 2 \sin \left( \frac{4 \pi x}{15} \right) \cos (96 \pi t)$,where $x$ and $y$ are in $cm$. The maximum number of loops that can be formed in it is