# Difference Between Constructive and Destructive Interference

## Main Difference – Constructive vs. Destructive Interference

Constructive and destructive interference are phenomena that take place when several waves meet. The main difference between constructive and destructive interference is that constructive interference occurs when the displacements of the waves that meet are in the same direction, whereas destructive interference occurs when displacements of the waves that meet are in the opposite directions.

## Principle of Superposition

Constructive and destructive interference occurs due to the principle of superposition. According to this principle, when several waves of the same type meet at a point, the resultant displacement at that point is the sum of the displacements due to each of the incident waves.

When two waves are meeting and the oscillations of the two waves are in the same stage, then we say the two waves are oscillating in phase. The phase difference between two waves that meet in-phase is a whole even-number multiple of pi (0, 2π, 4π,…). If the oscillations are at the opposite stages in the cycle, then we say that the waves are oscillating completely out-of-phase or in antiphase. The phase difference between two waves that are in antiphase is a whole odd-number multiple of pi (π, 3π, 5π,…).

## What is Constructive Interference

Constructive interference occurs when waves meet, having each of their displacements in the same direction. The result is that the displacements reinforce each other, forming a resultant wave with a higher amplitude than the amplitude of any of the waves that combine to produce it. The diagram below shows two waves meeting in phase to produce constructive interference:

Constructive interference between two waves in the same phase (shown in red and green. The resultant wave is shown in blue).

## What is Destructive Interference

When the waves that combine have their displacements in opposite directions, the resultant wave produced has a lower amplitude. In these cases, the interference is destructive. In the diagram below, the incident waves (shown in red and blue) which are in antiphase with each other, combine to form the blue resultant wave. If the amplitudes of the incident waves had been the same, the two would completely cancel each other out, and there would be no resultant wave (i.e. the resultant wave will have “zero amplitude”).

Destructive interference: two incident waves (red and green) which are in antiphase with each other meet, producing the blue resultant wave.

Noise-cancelling headphones rely on destructive interference: when a “noisy” sound wave is detected, the headphones emit a wave in antiphase with the noise. The two waves interfere destructively, effectively “cancelling out” the noise. Anti-reflective coatings in glasses work in the same way. The coating applied onto the glass reflect light from the glare back towards the glass, so that when the glare meets the “reflected glare”, they interfere destructively, cancelling out the glare.

Normal glass (left) compared with glass with an anti-reflective coating (right). The anti-reflective coating makes use of destructive interference of light waves in order to cancel out the glare.

## Interference Patterns

When waves from different sources meet, the interference at each point beyond the sources depends on the phase difference at each of those points. Due to the difference in the distances that the waves need to travel through to get to a particular place, the interference will be constructive in some places and destructive in others. The diagram below shows how two waves formed by two splashes in water interfere. The green and red circles show the wavefronts: i.e they show the positions of crests of the waves.

Interference patterns formed by two splashes in water.

When two crests meet (when a red line crosses a green line), constructive interference occurs and a larger crest is formed. This is shown in white in the above diagram. Some of these places are marked with “C”s. Where two troughs meet, the interference is again constructive. Here, deeper troughs form. These places are shown in black, and some of these places are marked with “T”s. When crests and troughs meet, the interference is destructive. These places form “blurred” regions on the water. Some of these regions are shown with a blue line.

## Difference Between Constructive and Destructive Interference

### Displacement of Incident Waves

When constructive interference occurs, the incident waves have displacements in the same direction.

When destructive interference occurs, the incident waves have displacements in the opposite directions.

### Amplitude of Resultant Waves

When constructive interference occurs, the amplitude of the resultant wave is larger than the amplitudes of the incident waves. Therefore, the intensity of the resultant waves is larger than the intensity of incident waves.

When destructive interference occurs, the amplitude of the resultant wave is smaller than the amplitudes of the incident waves. Therefore, the intensity of the resultant waves is smaller than the intensity of incident waves.

Image Courtesy:

“Simuliertes Interferenzbild zweier punktförmiger Quellen mit gleicher Wellenlänge…” by Dr. Schorsch (Own work) [CC BY-SA 3.0], via Wikimedia Commons

“This photo shows an antirelection coated window…” by Zaereth (Own work) [CC0 1.0], via Wikimedia Commons