Wave Interference - the principle of superposition

In summary, the conversation was about the Principle of Superposition and how to add the amplitudes of two interfering waves with different widths. The solution suggested adding the amplitudes, and a clarification was requested for question 2.
  • #1
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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  • #2
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.
 
  • #3
What do you mean? I don't follow
 

FAQ: Wave Interference - the principle of superposition

1. What is wave interference?

Wave interference is the phenomenon where two or more waves meet and interact with each other, resulting in a combined wave that is a sum of the individual waves.

2. What is the principle of superposition in wave interference?

The principle of superposition states that when two or more waves meet, the resulting displacement at any point is the algebraic sum of the individual displacements of the waves at that point.

3. How does constructive interference occur?

Constructive interference occurs when two waves meet and their amplitudes add together, resulting in a wave with greater amplitude. This can happen when the waves are in phase, meaning their crests and troughs align with each other.

4. What is destructive interference?

Destructive interference occurs when two waves meet and their amplitudes cancel each other out, resulting in a wave with a smaller amplitude or no wave at all. This can happen when the waves are out of phase, meaning their crests and troughs do not align with each other.

5. How does the principle of superposition apply to real-life situations?

The principle of superposition can be seen in many real-life situations, such as when two sound waves from different sources meet and interfere with each other, or when two ocean waves collide and form a larger wave. It is also used in various technologies, such as noise-canceling headphones, which use destructive interference to cancel out unwanted noise.

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