Meaning of Phase in stationary waves

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Discussion Overview

The discussion revolves around the meaning of phase in the context of stationary (standing) waves, particularly focusing on the statement that "in a standing wave, all the particles are in the same phase." Participants explore the implications of this statement, the mathematical representation of phase, and the differences between standing and progressive waves.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question the meaning of all particles being in the same phase, given that different particles have different positions (x values) in a standing wave.
  • Others suggest that the statement refers to the time-dependent factor in the wave equation, where the phase of the time-dependent part remains constant across all positions.
  • It is noted that every point in a loop (between adjacent nodes) is in phase with every other point in that loop, while being in antiphase with points in adjacent loops.
  • Participants discuss the distinction between two types of phase: one comparing distinct waves and another comparing points within the same wave.
  • One participant asserts that the formula provided by another gives the phase for a progressive wave, indicating a misunderstanding of the context of standing waves.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of phase in standing waves, with no consensus reached on the implications of the phase statement or the correctness of the formulas discussed.

Contextual Notes

There are unresolved questions regarding the definitions of phase in different contexts and the implications of the mathematical representations provided. The discussion highlights the complexity of phase relationships in wave mechanics.

zorro
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What is the exact meaning of the statement " In a standing wave, all the particles are in the same phase "?

Phase, ϕ = 2(pi)x/λ
If we consider the node as origin, different particles have different x values.
Then how come the phase is same for all?
 
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They likely mean the time-dependent factor, since the displacement in the standing wave is given by

[tex]sin(\omega t)sin(kx)[/tex]

The phase of the second factor depends on position, but the phase of the first factor does not.
 
Abdul Quadeer said:
What is the exact meaning of the statement " In a standing wave, all the particles are in the same phase "?

Phase, ϕ = 2(pi)x/λ
If we consider the node as origin, different particles have different x values.
Then how come the phase is same for all?

Every point in a loop(between adjacent nodes) is in phase with every other point in that loop and in antiphase with points in adjacent loops.
 
K^2 said:
They likely mean the time-dependent factor, since the displacement in the standing wave is given by

[tex]sin(\omega t)sin(kx)[/tex]

The phase of the second factor depends on position, but the phase of the first factor does not.

What is the difference between the two phases?

Every point in a loop(between adjacent nodes) is in phase with every other point in that loop and in antiphase with points in adjacent loops.

Please explain what's wrong in the formula I gave?
 
Abdul Quadeer said:
What is the difference between the two phases?



Please explain what's wrong in the formula I gave?

Your formula gives the phase for a progressive wave
 
Dadface is quite correct.

For progressive waves the term phase has two meanings.

1) You can compare the phase difference of two distinct waves as the difference in time between when each wave reaches a positive going maximum.

2) You can compare the phase difference between two points in the same wave. This is the difference in time between when each point reaches its positive going maximum.

For a standing wave all points between two successive nodes reach their positive maximum at the same time so the phase difference is zero, ie they are in phase.
 
Thanks!
 

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