2.3 Interference of waves from incoherent sources

1.1 Principle of superposition

2.1 Relation between phase difference $\left( \phi \right)$ and path difference $\left( {\Delta x} \right)$
2.2 Interference of waves from coherent sources
2.3 Interference of waves from incoherent sources
2.4 Reflection and transmission of a wave
2.5 Motion of wave during reflection
2.6 Expression for the reflection and transmission of wave

3.1 Transverse stationary wave on a stretched string
3.2 Vibrations in a stretched string
3.3 Melde's Experient
3.4 Resonance

4.1 Open organ pipe
4.2 Closed organ pipe
4.3 End correction
4.4 Resonance tube
4.5 Energy in a stationary wave

If the sources are incoherent, the phase difference between the sources keeps on changing.

At any point $P$, sometime constructive and sometime destructive interference takes place.

If the intensity due to each source is $I$, the resultant intensity at any point varies between $4I$ and zero. So, the average observable intensity at any point is $2I$

If the intensities due to individual sources is $I_1$ and $I_2$. The resultant intensity is,$$I = {I_1} + {I_2}$$

Therefore, no interference effect is observed for incoherent waves.

Note: For observable interference, the source must be coherent.