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Coherent and Incoherent Addition of Waves

Understanding Coherent and Incoherent Addition of WavesMeta description- This article discusses the addition of coherent and incoherent waves. It also details constructive and destructive interference.

Radiation from coherent sources is responsible for stable interference patterns produced when a single beam of light gets separated into two or more beams of light. Coherent waves have the same frequency and zero or constant phase difference. Incoherent waves have random frequencies and phase differences.

The addition of waves deals with the interference patterns created by the superposition of two waves. Coherence can be defined as a set relationship between the phases of waves during a beam of radiation of one frequency. Two light beams can be called coherent if the phase distinction between their waves is constant; they’re noncoherent if there’s a random or dynamic phase relationship.

Superposition Principle

The principle of superposition says:

  • When two waves collide, the subsequent removal of the medium at any point is equal to the algebraic sum of the singular waves’ displacements at that point.

  • Positive or negative singular wave relocations are possible. In the event that the removals are vectors, the total is calculated using vector expansion.

  • Interference, diffraction, and standing waves are all examples of peculiarities that can be explained using superposition. It works for all types of waves (sound waves, water surface waves, electromagnetic waves).                            

Coherent sources and incoherent sources

Coherent sources: The waves formed by coherent sources move in a continuous phase difference with time. Coherent sources can be classified into two types.

Temporal Coherence and Spatial Coherence

Incoherent sources: The waves formed by these sources will keep changing the phase difference with time. 


Interference is a phenomenon in which two waves collide and shape a subsequent influx of more prominent, lower, or similar abundantness. Interference impacts can be seen with a wide range of waves, for instance, light, radio, acoustic, surface water waves, gravity waves, or matter waves.

Constructive Interference 

  • When two waves come close enough together, their belongings combine. If the peaks, or most elevated parts of the waves, perfectly line up, the consolidated wave’s peak will be the sum of the two distinct peaks’ statutes.

  • Similarly, if the most reduced pieces of the waves (the box) line up perfectly, the joined box will be the consolidated profundity of the two distinct troughs.

  • This is known as constructive Interference, in which two floods (of similar frequency) communicate to adjust to each other, resulting in a new wave that is larger than the first.

Destructive Interference 

However, if two waves are not perfectly aligned, the peak of one wave will be dragged somewhere near the box of the other wave as it travels.

The peaks of the following, joined wave will be more limited than the peaks of either individual wave, and the troughs will be shallower than the troughs of both approaching waves. Destructive Interference is the term for this.

Locus of point

If we have two rational sources, S1 and S2, vibrating in stages for an erratic point P at any point along the way difference, S1P – S2P = mλ (m = 0, 1, 2, 3,…).

Interference will be constructive.

The sign between S1P and S2P addresses the contrast somewhere in the range of S1P and S2P, and the resultant force will be 4I0. However, assuming that the point P is with the goal of contrasting the way, S1P S2P = (m+ 1/2)λ, (m = 0, 1, 2, 3,…). , 2 and 3 are the loci of the point for which S1P – S2P is equivalent to nothing.

Addition of two waves

The evolution of two waves emanating from two sources with I1 and I2 powers. Because these two waves collide, the power of the subsequent wave will be as shown in the accompanying association.

I = I1+ I2 + 2(I1I2cos⁡p)½

Where p is the phase difference between two waves.

For the constructive Interference, the worth of p= 0°, with the goal that the cos p = 1 and

for the destructive Interference, the worth of p = 90°, with the goal that the cos p = 0.

Characteristics of coherent sources

  • The coherent waves have a steady phase contrast.

  • Waves are of one frequency.

  • The amplitude of the waves should be something very similar.


When two waves of the same type collide at a point in space, the resultant relocation is the vector sum of the displacements that the two waves would have delivered independently by that point. The term “impedance” refers to the superposition of at least two coherent waves in space to produce districts of maxima and minima.


Frequently asked questions

Get answers to the most common queries related to the CBSE Class 11th Examination Preparation.

Explain the term coherent sources?

Ans : The waves formed by coherent sources move in a continuous phase difference with time....Read full

Define destructive Interference?

Ans : Destructive Interference happens when the maxima of two waves are 180 degrees out of stage: a...Read full

What are the types of coherent sources?

Ans : Coherent sources are classified as-  ...Read full

What do you understand by the word Interference?

Ans : Interference is a peculiarity whereby two waves superpose to shape a resultant influx of more...Read full

What will be the intensity of the addition of two waves?

Ans : The evolution of two waves emanating from two sources with I...Read full