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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1. What are two waves in phase?

Two waves in phase refer to two waves that have the same frequency, wavelength, and amplitude, and are in perfect alignment with each other. This means that the peaks and troughs of the two waves occur at the same time and location, resulting in a constructive interference pattern.

2. How can two waves be in phase?

Two waves can be in phase if they have the same frequency, wavelength, and amplitude. This can be achieved by either starting the waves at the same time, or by adjusting the properties of one of the waves, such as its amplitude or frequency, to match the other.

3. What is the significance of exploring the possibility of two waves in phase?

Exploring the possibility of two waves in phase can help us understand the concept of interference and how it affects the behavior of waves. It also has practical applications in fields such as acoustics, optics, and electronics, where wave interference is utilized for various purposes.

4. How can we represent two waves in phase using graphs?

Two waves in phase can be represented using a graph by plotting the displacement of each wave over time. The two waves will have the same frequency, wavelength, and amplitude, and will overlap perfectly, resulting in a graph with a larger amplitude than either individual wave.

5. What is the difference between two waves in phase and two waves out of phase?

Two waves in phase have the same frequency, wavelength, and amplitude, and are in perfect alignment, resulting in a constructive interference pattern. Two waves out of phase, on the other hand, have the same frequency and wavelength, but their amplitudes are opposite, resulting in a destructive interference pattern.

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