How Can Two Waves with Different Amplitudes Be in Phase?

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Discussion Overview

The discussion revolves around the concept of phase in waves, specifically addressing how two waves with different amplitudes can be considered in phase. Participants explore the definitions of phase and amplitude, and seek visual representations to clarify their understanding.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions how two waves can be in phase if they have different amplitudes, prompting a request for visual examples.
  • Another participant explains that phase refers to the time axis, indicating that waves can be in phase regardless of amplitude differences, using the example of Sin(x) and 1+2*Sin(x).
  • A participant acknowledges that while the nodes of the waves remain aligned, the wave with greater amplitude appears vertically stretched.
  • One participant expresses uncertainty about the definitions of waves and phase, providing examples of sine waves with varying amplitudes and discussing the concept of phase in relation to frequency.
  • There is a suggestion that two waves of different frequencies might be considered in phase based on their combined envelope's amplitude, though this definition is noted as potentially ambiguous.
  • A later reply expresses gratitude for the clarification and mentions a preference for diagrams to aid understanding.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definitions of phase and amplitude, and there are multiple interpretations of how these concepts interact. The discussion remains unresolved regarding the implications of amplitude on phase.

Contextual Notes

Some participants express uncertainty about the definitions and implications of phase and amplitude, indicating that assumptions may vary. The discussion includes references to sine waves and composite waves, but lacks clarity on how these examples definitively relate to the original question.

Graffite
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May I know how is it possible for two waves to be in phase when they have different amplitude? I couldn't find any existing graphs that clearly shows how the two waves are in phase, would anyone be able to sketch it out so I can have a look. Thank you:smile:
 
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Welcome to PF.

Phase refers only to the time axis.
If you plot Sin(x) and 1+2*Sin(x) the waves will still be in phase, but one will be scaled and shifted vertically.
 
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OHH therefore the nodes of both waves will still be on the same spot, but the wave will be stretched vertically! Thank you
 
Graffite said:
May I know how is it possible for two waves to be in phase when they have different amplitude?
I'm not sure what you mean by waves, nor, for that matter, phase! However, here are
-two sine waves, one with an amplitude 0.7 of the other
-two sine waves, one with an amplitude 0.7 of the other and time shifted by 1 cycle/ 2pi
- a composite wave comprising a fundamental and a third harmonic with an amplitude of 0.3 of the fundamental
- a composite wave with 0.7 times the amplitude of the above and both fundamental and third harmonic time shifted by 1 cycle/2pi
phase.png

If two waves have the same amplitude at all times, they are not just in phase, but are identical.
If two sinewaves are in phase, I can't see where amplitude has any bearing on it.
Maybe two waves of different frequency are sometimes said to be in phase when their combined envelope has a greater amplitude than either wave, or out of phase when the sum is less than either, but I think it is not well defined.
 
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Merlin3189 said:
I'm not sure what you mean by waves, nor, for that matter, phase! However, here are
-two sine waves, one with an amplitude 0.7 of the other
-two sine waves, one with an amplitude 0.7 of the other and time shifted by 1 cycle/ 2pi
- a composite wave comprising a fundamental and a third harmonic with an amplitude of 0.3 of the fundamental
- a composite wave with 0.7 times the amplitude of the above and both fundamental and third harmonic time shifted by 1 cycle/2pi
View attachment 325377
If two waves have the same amplitude at all times, they are not just in phase, but are identical.
If two sinewaves are in phase, I can't see where amplitude has any bearing on it.
Maybe two waves of different frequency are sometimes said to be in phase when their combined envelope has a greater amplitude than either wave, or out of phase when the sum is less than either, but I think it is not well defined.
thank you so much it helped me understood a lot!
 
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Glad it helped. I always like diagrams and pictures to help me understand.
 
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