Undergrad How Can Two Waves with Different Amplitudes Be in Phase?

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SUMMARY

Two waves can be in phase despite differing amplitudes, as phase refers solely to their time alignment on the axis. For example, plotting Sin(x) and 1+2*Sin(x) demonstrates that both waves maintain their nodes at the same positions while one wave is vertically scaled. The discussion highlights that amplitude does not affect the phase relationship between sine waves, and even composite waves can exhibit this characteristic when time-shifted appropriately.

PREREQUISITES
  • Understanding of wave properties, specifically phase and amplitude
  • Familiarity with sine wave functions and their graphical representation
  • Basic knowledge of harmonic waves and their interactions
  • Ability to interpret wave diagrams and sketches
NEXT STEPS
  • Study the mathematical representation of sine waves and their phase relationships
  • Explore the concept of wave superposition and its effects on amplitude
  • Learn about harmonic analysis and how to construct composite waves
  • Investigate the implications of time shifts on wave behavior and phase alignment
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Students of physics, audio engineers, and anyone interested in wave mechanics and signal processing will benefit from this discussion.

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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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!
 
Glad it helped. I always like diagrams and pictures to help me understand.
 

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