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

$A$ wave is represented by the equation $y = 10 \sin 2\pi(100t - 0.02x) + 10 \sin 2\pi(100t + 0.02x)$. The maximum amplitude and loop length are respectively:

The transverse displacement of a string (clamped at both ends) is given by $y(x, t) = 0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The length of the string is $1.5 \; m$ and its mass is $3.0 \times 10^{-2} \; kg$. Answer the following:
$(a)$ Does the function represent a travelling wave or a stationary wave?
$(b)$ Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength,frequency,and speed of each wave?
$(c)$ Determine the tension in the string.

$A$ standing wave is established in a single loop. At $t = 0$,the kinetic energy $(K.E.)$ of the string is zero. Choose the correct option.

Stationary waves of frequency $300\, Hz$ are formed in a medium in which the velocity of sound is $1200\, m/s$. The distance between a node and the neighbouring antinode is ... $m$.

$A$ 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 $Å$)