Wave interference occurs when two waves, both travelling in the same medium, meet. Depending on the phase of the waves that meet, constructive or destructive interference can occur.
The Principle of Superposition
The Principle of Superposition – when two or more waves, travelling through the same medium, interfere the displacement of the resultant wave is the sum of the displacements of the original waves at the same point.
For example if a wave has a displacement of +1 and another wave has a displacement of +2 at the same point the resultant wave will have a displacement of +3.
As another example, if a wave has a displacement of +2 and another wave has a displacement of -1 at the same point the resultant wave will have a displacement of +1.
This is done at every point along the wave to find the overall resultant wave.
Constructive Interference
Constructive interference occurs when two waves meet that are in phase with each other. In other words, when the displacement of both waves is in the same direction they constructively interfere. The amplitude of the resultant wave is greater than that of the individual waves.
Pure constructive interference occurs when the crests and troughs both match up perfectly.
In the diagram below, the green line represents two waves moving in phase with each other. Only one colour is shown because they are in phase with each other and so each point on the second wave is at exactly the same point as the first.
The red line shows the resultant wave:
As the two waves have exactly the same amplitude, the resultant amplitude is twice as big. The crests are twice as high and the troughs are twice as deep. The wavelength is exactly the same.
Constructive interference can also occur when the two waves don’t have exactly the same amplitude.
Destructive Interference
Destructive interference occurs when two waves meet that are in antiphase with each other. In other words, when the displacement of both waves is in opposite directions they destructively interfere. The amplitude of the resultant wave is smaller than that of the individual waves.
Pure destructive interference occurs when the crests of one wave align with the troughs of the other.
In the diagram below two waves, one green and one blue, are shown in antiphase with each other. The peaks of the green wave align with the troughs of the blue wave and vice versa.
The red line shows the resultant wave:
The magnitude of the crests on the green wave are equal the the magnitude of the troughs on the blue wave. Displacement has direction and so when added the two cancel each other out. The resultant wave has zero amplitude.
Quite often when two waves meet they don’t perfectly align to allow for only constructive or destructive interference. There may be points along the resultant wave where constructive interference occurs and others where they interfere destructively.
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