Question

In a stationary wave all the particles:

Answer 1

Hint:Stationary waves are also known as standing waves. These waves are created by superposition of two waves having the same frequency and amplitude but moving in the opposite direction of each other.

Complete answer:
Standing waves are a superposition of two waves moving in opposite directions each having the same amplitude and frequency. This is the result of interference i.e., when waves are superimposed, their energies are either added up or cancelled. Standing waves are also known as stationary waves.

The particles do not move along a wave but they simply oscillate up and down about their individual mean positions as the wave passes by. A node is a point on standing wave where the wave has minimum amplitude and antinode is a point on standing wave where the wave has maximum amplitude. Nodes are points of zero amplitude and appear to be fixed.

The amplitude is given by the function $2a\sin (kx)$. Between two nodes the sign of $\sin (kx)$ is the same, only its value changes. So, the displacement of the particles between two nodes is in the same direction, only the magnitude differs. This concludes that the particles between two nodes are moving in the same phase.

In a stationary wave all the particles in a particular region between two nodes vibrate in the same phase, and the particles on the different sides of a node differ by a phase difference of $\pi $. The particles in the adjacent segments vibrate in opposite phases. Thus, alternate antinodes vibrate in the same phase.

Note: The distance between any two consecutive nodes or antinodes is equal to $\dfrac{\lambda }{2}$ while the distance between any node and its adjacent antinode is equal to $\dfrac{\lambda }{4}$. The opposite of a node is an antinode, a point where the amplitude of the standing wave is a maximum. These occur midway between the nodes.