With this simulation, you can explore the interference pattern that results from the superposition of two sources of waves. The simulation models what happens with two speakers, emitting sound waves; with two oscillating bobbers in a water tank, producing water waves; or, with two light sources, so the interference is with two light waves.
In the simulation, red regions are areas where the net displacement is positive (such as when two peaks overlap) and blue regions are areas where the net displacement is negative (such as when two troughs overlap). In the black regions, the net displacement is zero, or close to zero.
To understand this pattern, we use the idea of the path-length difference. There is a movable yellow-point in the simulation. The path-length difference (∆L) for this point is the distance the point is from one of the sources minus the distance the point is from the other source. These distances are expressed in units of the wavelength. When the sources send out waves that are in phase with one another, the waves will interfere completely constructively when the path-length difference is an integer number of wavelengths, and they will interfere destructively when the path-length difference is an integer number of wavelengths, plus half a wavelength. We can express this in the form of equations.
When the sources are in phase
condition for constructive interference: ∆L = m λ, where m = 0, 1, 2, ...
condition for destructive interference: ∆L = (m + 0.5) λ, where m = 0, 1, 2, ...