I was going though the derivation of intensity of waves from coherent sources for constructive and destructive interference:
Suppose you have two sources that are at the same frequency and have the same amplitude and phase but are at different locations. One source might be a distance $x$ away from you and the other a distance $x+\Delta x$ away from you. The waves from these two sources add like: $\displaystyle s(x,t)$ $\textstyle =$ $\displaystyle s_0 \sin(k x - \omega t) + s_0 \sin(k (x + \Delta x) - \omega t)$
The resultant wave at any point is given by
Now as I(Intensity) ∝ $A^2$,This equaion can be written as
EDIT: Coherent sources have same frequency but they can have varying wavelength so why is wavelength assumed equal here?