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Question
Which of the following statements are true for a stationary wave?
- Every particle has a fixed amplitude which is different from the amplitude of its nearest particle.
- All the particles cross their mean position at the same time.
- All the particles are oscillating with same amplitude.
- There is no net transfer of energy across any plane.
- There are some particles which are always at rest.
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Solution
a, b, d and e
Explanation:
We know that the standard equation of stationary wave is
`y(x, t) = 2a sin (kx) cos (ωt)`
In stationary waves, the particles between the two nodes vibrate with different amplitudes. The amplitude increases from node to antinodes from zero to maximum and then from antinodes to nodes amplitude decreases from maximum to zero. The amplitude of a particle will remain constant, but the amplitude will vary with λ.
∴ `k = (2π)/λ`. This verifies option (a) and rejects option (c).
The particles present at nodes have amplitude zero. Hence, verifies option (e).
We know that particles at nodes are at rest. Therefore, there is no energy transfer. This verifies option (d).
Particles between the two nodes are in the same phase, it means the motion of particles will be either upward or downward. Thus, particles will cross the mean position at the same time. This verifies option (b).
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