Wave Interference - the principle of superposition

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SUMMARY

The discussion centers on the Principle of Superposition, which states that the amplitudes of two interfering waves are summed when they coincide. The user seeks clarification on how to determine the shape of the resulting wave when the waves have different widths. The solution involves adding the amplitudes of the waves at corresponding points, but the user expresses confusion about visualizing the resulting wave's shape. The discussion highlights the need for a deeper understanding of wave interference, particularly with varying wave widths.

PREREQUISITES
  • Understanding of wave properties, including amplitude and width
  • Familiarity with the Principle of Superposition in wave theory
  • Basic knowledge of wave diagrams and graphical representation of waves
  • Experience with mathematical addition of values in the context of physics
NEXT STEPS
  • Research how to graphically represent wave interference with varying widths
  • Study the mathematical modeling of wave functions in physics
  • Learn about Fourier analysis for decomposing complex waveforms
  • Explore practical applications of wave interference in acoustics and optics
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, educators teaching wave interference concepts, and anyone interested in understanding the graphical representation of wave interactions.

Element1674
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Homework Statement


The problems are attached in the photo below (or at least I'm hoping they are, doing this from my Ipad makes this somewhat diffcult)

Homework Equations


Not really an equation, but the Principle of Superposition states that the amplitude of two interfering waves are added together when they coincide.

The Attempt at a Solution


My instructor rushed through this concept and the homework (aside from the questions below) all involved waves of equal width (I'll just call that width value x). So all that needed to be done was to add the amplitude of the waves (AmpWaveA + AmpWaveB = Amplitude of resulting wave) where the resulting wave had the same width value of X. I'm just curious on how to do this for waves with different widths; I know I add their amplitudes, but I don't know what the shape of the resulting wave should be.

So my question is, how do I do question 2? The wave diagrams. Also sorry about the upside down picture, idk why it did that.
 

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Element1674 said:

Homework Statement


The problems are attached in the photo below (or at least I'm hoping they are, doing this from my Ipad makes this somewhat diffcult)

Homework Equations


Not really an equation, but the Principle of Superposition states that the amplitude of two interfering waves are added together when they coincide.

The Attempt at a Solution


My instructor rushed through this concept and the homework (aside from the questions below) all involved waves of equal width (I'll just call that width value x). So all that needed to be done was to add the amplitude of the waves (AmpWaveA + AmpWaveB = Amplitude of resulting wave) where the resulting wave had the same width value of X. I'm just curious on how to do this for waves with different widths; I know I add their amplitudes, but I don't know what the shape of the resulting wave should be.

So my question is, how do I do question 2? The wave diagrams. Also sorry about the upside down picture, idk why it did that.

Add their amplitudes. If the vertical displacement of a wave at one point is -1, and the corresponding vertical displacement of the other wave is 2, the overall vertical displacement is 1.
 
What do you mean? I don't follow
 

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