Two Waves In Phase: Exploring the Possibility w/ Graphs

In summary: Do you have a particular situation in mind?In summary, the conversation discusses the concept of phase in relation to waves with different amplitudes. It is possible for two waves to be in phase even with different amplitudes, as long as they are synchronized on the time axis. Graphs may not always clearly show this, but by plotting different scenarios, it can be seen that the nodes of both waves will still be in the same spot, but the vertical scale may differ. The conversation also touches on the idea of waves with the same amplitude being identical, and the potential for confusion in defining in-phase and out-of-phase for waves with different frequencies. A visual aid such as diagrams or pictures can be helpful in understanding these concepts.
  • #1
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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  • #2
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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  • #3
OHH therefore the nodes of both waves will still be on the same spot, but the wave will be stretched vertically! Thank you
 
  • #4
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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  • #5
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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  • #6
Glad it helped. I always like diagrams and pictures to help me understand.
 
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Related to Two Waves In Phase: Exploring the Possibility w/ Graphs

What does it mean for two waves to be in phase?

When two waves are in phase, their crests and troughs align perfectly. This means that the peaks (maximum points) and valleys (minimum points) of the waves occur at the same points in space and time. As a result, the waves reinforce each other, leading to constructive interference and a resultant wave with greater amplitude.

How can graphs help in understanding waves in phase?

Graphs provide a visual representation of wave behavior. By plotting two waves on the same graph, one can easily observe whether their peaks and troughs align. When the waves are in phase, the graph will show their corresponding points coinciding, making it easier to understand the concept of constructive interference and the resultant wave's increased amplitude.

What is constructive interference?

Constructive interference occurs when two or more waves overlap and their amplitudes add together. This happens when the waves are in phase, meaning their peaks and troughs align. The result is a new wave with a higher amplitude than any of the individual waves, leading to a more pronounced wave pattern.

Can two waves of different frequencies be in phase?

Two waves of different frequencies can be temporarily in phase at certain points, but they will not remain in phase consistently. Due to their different frequencies, the alignment of their peaks and troughs will shift over time, leading to alternating periods of constructive and destructive interference. For sustained in-phase conditions, the waves must have the same frequency.

What are the practical applications of waves being in phase?

Waves being in phase have several practical applications, including in sound engineering, telecommunications, and optics. For instance, in sound engineering, aligning sound waves in phase can amplify audio signals, enhancing sound quality. In telecommunications, phase alignment is crucial for signal clarity and strength. In optics, coherent light sources like lasers rely on waves being in phase to produce focused and intense beams of light.

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