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Interference

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Interference

When two waves superimpose one over the other, their sum produces a different wave in terms of amplitude. This new wave has a different mathematical representation and results in a different shape.

Types of interference

The attributes of a wave are the amplitude ‘A’, the frequency ‘f’, and the phase ‘θ’. The amplitude indicates the excursion of the wave, the frequency is the number of oscillations per unit time (usually a second), and the phase is the position of the wave in space relative to a reference point.

To clarify the ideas and concepts behind amplitude, frequency, and phase, let’s examine an example where we have the sinusoidal functions sin (x) and sin (x + π/2). Both have the same shape because the amplitude and frequency are the same. But let’s have a look at their graphs:

Interference. Sin waves interference. StudySmarterFigure 1. Sin (x) (red) and sin (x + π/2) (black). Source: Oğulcan Tezcan, StudySmarter.

The phase is different, which causes a backward shift of the second wave (in black). We notice the shift because the point where the function passes from zero isn’t the origin anymore. This is very important because it changes the way the waves overlap.

We study phase differences with the help of a reference point. In the graph above, the reference point is taken as zero. The phase angle of the red wave sin (x) is zero and can be shown as sin (x+0). The starting point of the wave, therefore, is the same as the reference point with no phase difference.

For the black wave, however, the phase difference is positive (+ π/2), which means that the origin of the wave (its starting point) is said to be ‘before’. On the graph, it can be seen to the left of the reference point. When the phase difference is negative, the origin of the wave is said to be ‘after’ the reference point. On the graph, it would, therefore, be to the right of the reference point.

Constructive and destructive interference

If we add up two identical waves, the resulting amplitude doubles:

sin (x) + sin (x) = 2 sin (x)

While mathematically obvious, have a look at what it means visually, with two sinusoids one above the other, as in figure 2.

Interference. Sin waves. StudySmarterFigure 2. Two sin (x) functions translated above and below the x-axis. Source: Oğulcan Tezcan, StudySmarter.

The points that have the same x coordinate also have the same amplitude. Applying the sum causes the wave to stretch. Where the amplitude was 1, it is now 2, and where it was -1, it is now -2. This is called constructive interference. An example from everyday life is two speakers playing the same track. The volume of the music perceived is maximum when the waves produced by the speakers are in phase, interfering constructively.

When the waves have different phases, the result of the superposition changes, especially if they are in phase opposition or counter-phase when every point is added to one of the opposite value, e.g., 1 + (-1), as in the graph below.

Interference. Sum of sin waves. StudySmarterFigure 3: Sin (x - π/2) (blue), sin (x + π/2) (red). Their sum is a straight line. Source: Oğulcan Tezcan, StudySmarter.

The sum of these waves is zero due to destructive interference. Notice how, in this case, the phase causes the same result as the negative sign before the function.

sin (x - π / 2) + sin (x + π / 2) = 0

sin (x - π / 2) - sin (x - π / 2) = 0

We defined the two ends of the line. In between, there are all the combinations of the two waves. The phase of the resulting wave is shifted to somewhere between the phases of the interfering waves, depending on their amplitudes, and the value of its amplitude will be between zero and twice the amplitude of the interfering waves.

Interference. Sum of Sin waves. StudySmarterFigure 4: Sin (x - π/2) (blue), sin (x) (red), and their sum (green). Source: Oğulcan Tezcan, StudySmarter.

Interference patterns

We talked about the interference between one-dimensional waves. The same phenomenon occurs when the propagation happens along two or more dimensions. In this case, two waves interfere and create an interference pattern.

When two stones are thrown into a lake, with one being thrown from a slightly different spot close to the one from which the first stone was thrown, a bi-dimensional wave forms on the surface of the water. In this scenario, the surface of the water gets corrugated but still exhibits a regularity, hence the name of this type of interference.

Interference. Position of the wave source. StudySmarterFigure 5: In the case of a bi-dimensional wave, the position of the source (the point from where the stone is thrown) influences the pattern as well. Notice how the waves are much more corrugated near the sources and almost unaffected moving away from them. Source: Admitter, Flickr (CC BY-ND 2.0).

In the image, two circular waves propagate towards each other at an angle of π/2. The wave fronts interfere almost orthogonally, giving the water a grid-shaped surface. The lines of the grid are points of destructive interference, while between them, there are points of constructive interference.

Interference - key takeaways

  • When we say that two waves are superimposed or interfere, we are talking about the same phenomenon.
  • The interference can be constructive or destructive, but generally speaking, the interference will be a combination of the two.
  • The phenomenon of interference occurs in any case, with the propagation on one or more dimensions. In the latter case, we speak of interference patterns.

Frequently Asked Questions about Interference

Destructive interference is the kind of interference that causes two waves to subtract each other.

Interference is the phenomenon that occurs when two waves collide with each other.

Interference is when two waves collide with each other. There are two types of interference: constructive and destructive interference.

Two waves collide, creating a wave that is the sum of the two.

Final Interference Quiz

Question

If we add up two identical waves, which of the following will happen?

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Answer

The resulting amplitude will double.

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Question

If two waves with the same amplitudes are in phase opposition, what will be their resulting amplitude?

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Answer

Zero.

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Question

When two waves in phase opposition interfere with each other, what kind of interference occurs?

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Answer

Destructive interference.

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Question

When the propagation happens along two or more dimensions, two waves interfere and create …

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Answer

An interference pattern.

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Question

Which of the following is a definition for the frequency of a wave?

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Answer

It is the number of oscillations per unit time.

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Question

When two or more waves overlap each other at one point, the total displacement caused at that point is the sum of individual displacements caused by the waves at that point.


What is the name of this phenomenon?

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Answer

Superposition.

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Question

What are the three characteristics that describe a wave?

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Answer

Amplitude, frequency, and phase.

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Question

Is the interference influenced by the phase?

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Answer

Yes, it is.

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Question

Does the interference occur only between one-dimensional waves?

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Answer

No, it occurs for all types of waves.

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Question

Do two rocks thrown into a lake close to each other generate an interference pattern?

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Answer

Yes, they do.

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Question

If two sinusoidal waves of the same amplitude, frequency, and phase interfere, does the resulting wave have a different phase?

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Answer

No, it has the same phase.

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Question

What happens when the interference is not completely constructive or destructive?

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Answer

The resulting wave has an amplitude and a phase different from the two waves that have interfered.

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Question

What is the interference called when two identical waves are in opposition of phase?

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Answer

Destructive interference.

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Question

When two waves are superimposed, what happens to the single point of each one?

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Answer

Every point of a wave is added to the corresponding point of the other.

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Question

In Physics, are the sum of two waves and the interference the same thing?

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Answer

Yes, they are.

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