Standing stationary waves can be obtained in an air column even if the interfering waves are

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 .... $cm$.

$A$ string of length $0.5 \text{ m}$ and mass $10^{-3} \text{ kg}$ is tightly clamped at its ends. The tension in the string is $0.8 \text{ N}$. Identical wave pulses are produced at one end at equal intervals of time $\Delta t$. What is the minimum value of $\Delta t$ which allows constructive interference between successive pulses (in $\text{ s}$)?

$A$ progressive wave travelling in the positive $x$-direction given by $y=a \cos (k x-\omega t)$ meets a denser surface at $x=0, t=0$. The reflected wave is then given by

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

Explain the reflection of a wave at a rigid support.