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Interference and superposition

Interference is the phenomenon which results when two or more waves meet. These waves "combine" at the points that they meet, producing distinct patterns.

The principle of superposition helps to understand the pattern resulting from interference.

The principle states that the net displacement caused by two or more waves that meet is equivalent to the sum of the displacements produced by the individual waves. These waves "combine" and form a resultant wave.

Consider two waves: A and B. Wave A and wave B meet at a particular point at a particular time.

Wave A produces a displacement $$a$$ at that point. Wave B produces a displacement $$b$$ at that point. The net displacement at that point would be then be equal to $$a+b$$.

According to the principle of superposition, the total displacement caused by two waves is the sum of the displacements of both waves.
According to the principle of superposition, the total displacement caused by two waves is the sum of the displacements of both waves.

Destructive interference occurs when the net displacement after the superposition of two waves is lower than the individual displacement caused by either wave.

Conversely, constructive interference occurs when the net displacement after the superposition of two waves is higher than the individual displacement caused by either wave.

According to the principle of superposition, the total displacement caused by two waves is the sum of the displacements of both waves.
According to the principle of superposition, the total displacement caused by two waves is the sum of the displacements of both waves.

Waves or sources with a constant phase difference at all times are called coherent.

Two coherent waves have the same frequency and wavelength. A constant phase difference cannot occur if the waves had different frequencies and wavelengths.

Perfect constructive interference occurs when the crests of two coherent waves align exactly. This means that the two waves are in phase (i.e. they have a phase difference of zero).

The resultant wave of two perfectly constructively interfering waves has the highest possible amplitude.

If two perfectly constructively interfering waves have the same amplitude, the resultant wave would have double the amplitude of an individual wave.

Perfect constructive (left) and perfect destructive (right) interference. The resultant waves are at the top.
Perfect constructive (left) and perfect destructive (right) interference. The resultant waves are at the top.

Perfect destructive interference occurs when the crests of one wave aligns with the troughs of another wave which is coherent with the first wave. This means that the two waves are exactly $$\pi$$ radians out of phase (i.e. in anti-phase).

The resultant wave has the smallest possible amplitude. If the two waves have the same amplitude, they "cancel" each other out (i.e. there will be no wave in the region that they meet).

The word "perfect" is often omitted when describing perfect constructive and destructive interference as extreme cases of interference are more easily observed.

Perfect constructive (left) and perfect destructive (right) interference. The resultant waves are at the top.
Perfect constructive (left) and perfect destructive (right) interference. The resultant waves are at the top.