why are coherent sources necessary to produce a sustained interference pattern?

b/c for getting a sustained interference pattern, we need two waves having constant phase difference between them.two waves can be two displacement sine waves and two pressure sine waves or can be two electromagnetic wave or two matter waves or two elastic waves. y1(x, t) =
Asin(kx - wt) y2(x, t) =
Asin(kx - wt + $ ) where $ is constant phase difference b/w waves. this type of waves can be produced by only coherent sources.