As we know, if we superpose two coherent sources of intensities $I_1$ and $I_2$, the resultant intensity is not merely equal to $I_1 + I_2$ but sometimes can be much less and much more than that value. On the other hand, most practical and common sources - the non coherent ones - if we superpose them, the resultant intensity is simply the algebraic sum of the respective intensities ($I_1 + I_2$).
Say there are two coherent sources producing some waves with a phase difference of $\pi/2$. The resultant amplitude is the square root of sum of squares of respective amplitudes. By this we can conclude that these coherent sources superimpose to produce a new intensity which is algebraic sum of respective intensities (just like the non-coherent sources).
My question is mathematically the reason of such an occurrence is justified, but how to physically justify and analyse the reason why two coherent sources suddenly behaved like a non coherent one?