The equation of a stationary wave is given by $y = 5 \cos \left( \frac{\pi x}{3} \right) \sin (40 \pi t) \text{ cm}$. What is the distance between two consecutive nodes in $\text{cm}$?

In a standing wave on a string rigidly fixed at both ends:

$A$ 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.

$A$ standing wave pattern is formed on a string. One of the waves is given by the equation $y_1 = a \cos(\omega t - kx + \pi/3)$. Find the equation of the other wave such that at $x = 0$,a node is formed.

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

Write the equation of a stationary wave and obtain the equations of nodes and antinodes by defining them.