From SHM to a wave. Each source is a mass on a spring that moves up and down in simple harmonic motion, y = A sin(ωt) with ω = 2π/T. Whatever the source does, the wave carries it outwards at the speed v of the medium. A point a distance x away repeats the source’s motion a time x/v later, so the shape of the wave at one instant is the history of the source, laid out in space:

y(x,t) = A sin(ωt − kx + φ), k = 2π/λ, λ = vT

Phase difference. The phase of an oscillation is the angle θ = ωt + φ₀ of the point going round the reference circle: the displacement is its height. Two oscillations of the same period differ by a constant phase difference φ. Here source 2 is ahead of source 1 by φ: it reaches every point in its motion earlier by a time Δt = φT/2π, which is a fraction φ/2π of a whole cycle. In the wave this shows up as a shift in distance: the crests of wave 2 are ahead of the crests of wave 1 by

Δx = φ λ / 2π (a phase difference of 2π is a whole wavelength)

Adding the waves. When two waves of the same size and frequency meet, they add. The result is again a wave with the same frequency and with amplitude 2A|cos(φ/2)|. In phase (φ = 0) the crests meet crests, and the sum has twice the amplitude (constructive interference). In antiphase (φ = π) the crests meet troughs and the sum is zero (destructive interference). The arrows in the phasor diagram add head to tail in the same way. The graph shows the amplitude of the sum for every phase difference.

The vertical scale is exaggerated (the wavelength is much longer than the amplitude). A phase difference can be given in radians, in degrees (π rad = 180°) or as a fraction of a cycle. Phase differences of φ and φ + 2π are the same thing.