For a stationary wave, $y = 12 \cos \left( \frac{\pi x}{10} \right) \sin(36\pi t) \text{ cm}$, the distance between a node and the successive antinode is (in $\text{ cm}$)

$A$ string fixed at both ends vibrates in $5$ loops as shown in the figure. The total number of nodes and antinodes respectively are

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

When a wave propagating on a string gets reflected from a fixed rigid support,what is the change in its phase?

Explain the reflection of a wave at a free support.

The equation of a stationary wave along a stretched string is given by $y = 5 \sin \left( \frac{\pi x}{3} \right) \cos (40 \pi t)$. Here $x$ and $y$ are in $cm$ and $t$ is in seconds. The separation between two adjacent nodes is: (in $cm$)