What you are looking at

Each source sends out a wave whose height at a distance r and time t is A·sin(2πf(t − r/v) + φ): amplitude A, frequency f, wave speed v, and a phase offset φ. The field you see is the sum of those heights from every source, coloured from trough (cyan) through node (dark) to crest (warm).

• Two sources at the same frequency and phase give the classic fan of fringes: the dark bands trace out the points where the distance to each source differs by exactly half a wavelength.
• Nudge one source's phase by half a cycle and every bright band swaps with a dark one.
• Raise the frequency and the fringes crowd together; raise the attenuation and distant sources fade, so the nearer one dominates.

This is the same maths behind the double-slit experiment, noise-cancelling headphones, and how a phased-array antenna steers a beam without moving.