Question

Which of the following statements is/are true regarding a stationary wave?

• A. All particles in a particular segment between two nodes vibrate in the same phase.
• B. Particles in the neighbouring segments vibrate in opposite phases.
• C. All the particles of the medium attain their maximum velocities simultaneously when they pass through their mean positions.
• D. All the particles of the medium, except those at nodes, execute simple harmonic motion about their mean positions.

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A All particles in a particular segment between two nodes vibrate in the same phase.
B Particles in the neighbouring segments vibrate in opposite phases.
C All the particles of the medium attain their maximum velocities simultaneously when they pass through their mean positions.
D All the particles of the medium, except those at nodes, execute simple harmonic motion about their mean positions.

A stationary wave has the following characteristics:

The maximum velocity is different at different points. Its value is zero at the nodes and gradually increases towards antinodes. All the particles attain their maximum velocities simultaneously when they cross their mean position.

Thus, the disturbance doesnt move in any direction. The conditions of crests and troughs merely appear and disappear in fixed positions in fixed intervals of time.

Particles belonging to a particular segment (crest or trough) vibrate in the same phase but the particles in the neighbouring segments vibrate in opposite phases.

It is clear that, except the particles at nodes, all the particles of the medium execute SHM about their mean position.

Thus, all the options are correct answers.