In villages, children love to play near the ponds.
we notice that when children throw a stone in the pond then a wave is generated.
Sometimes they throw two or more stones together and we notice that two different patterns are generated.
These patterns overlap on one another and move simultaneously.
They enjoy watching such patterns and keep throwing stones for fun.
The overlapping of these patterns and the nature of their movements is explained by the concept of coherent and incoherent waves.
Let's first discuss the waves and their superimposition.
A wave is a disturbance that transfers energy through space with little or no associated mass transfer.
It consists of oscillation or vibration of a physical medium.
The superimposition of two waves of amplitude A1​ and A2​ is provided by,
Now let's discuss the coherent and incoherent sources.
Let's consider we are touching the two needles on the water surface.
These needles will produce different patterns. The waves in these patterns will intersect each other.
If the velocity of both needles is same then the waves formed will be known as coherent and sources will be coherent sources.
So in the coherent sources, the phase difference between two waves will be zero or constant with time.
If the two waves are moving with different speed then pattern formed by them will vary.
Suppose the first needle is moving with constant rate and the second needle is moving with variable pace.
The interference formed by such waves will not be uniform or coherent, such waves will be known as incoherent waves and sources are called incoherent sources.
In the case of incoherent sources, the phase difference will keep changing with time.
This is all about the coherent and incoherent sources and how these sources are distinguished by the phase difference.
Revision
The coherent sources are those sources in which the waves formed will move with constant phase difference with time.
The incoherent sources are those sources in which the waves formed will keep changing the phase difference with time.