$A$ string is rigidly tied at two ends and its equation of vibration is given by $y = \sin(2\pi x) \cos(2\pi t)$. Then the minimum length of the string is .... $m$

$A$ travelling wave represented by $y = A \sin (\omega t - kx)$ is superimposed on another wave represented by $y = A \sin (\omega t + kx)$. The resultant 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 standing wave in a string fixed at both ends is given as $y = 2A \sin kx \cos \omega t$. The amplitude and frequency of a particle vibrating at the midpoint between an antinode and a node are respectively:

$A$ transverse displacement of a vibrating string is given by $y = 0.06 \sin \left( \frac{2 \pi}{3} x \right) \cos (120 \pi t)$. If the mass per unit length of the string is $4 \times 10^{-2} \ kg/m$,then the tension in the string will be: (in $N$)

$A$ 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 $Å$)