Interference

4 min read#waves

Two overlapping waves reinforce where their crests align and cancel where crest meets trough, painting a fixed pattern of bright and dark fringes.

Contents

Interference

Interference is the Superposition Principle made visible. When two waves overlap, their displacements add — but whether they reinforce or cancel depends on whether they arrive in step. Align crest with crest and you get constructive interference, doubling the amplitude. Align crest with trough and you get destructive interference, flat nothing. From two perfectly ordinary wave sources emerges a stable, sculpted pattern of loud and quiet, bright and dark.

Path difference sets the fringes

Consider two sources oscillating in phase, a distance apart, and a point that sits a distance r_1 from one and r_2 from the other. The two waves arrive having traveled different distances, so they are out of step by the path difference \Delta r = r_2 - r_1. The rule is entirely about how many wavelengths fit in that gap:

\Delta r = m\lambda \;\Rightarrow\; \textbf{constructive},\qquad \Delta r = \left(m+\tfrac12\right)\lambda \;\Rightarrow\; \textbf{destructive},

for integer m. The set of points with a constant path difference is a hyperbola, which is why the bright fringes fan out in smooth curves — visible directly in the ripple tank below.

A two-source ripple tank. Each source emits identical circular waves; the field is their sum. Bright violet bands are crests reinforcing (constructive), accent bands are troughs, and the gray channels between are nodal lines where the waves cancel. Move the mouse left/right to change the source spacing and watch the fringes fan.

Coherence

The pattern only stays still if the two sources keep a fixed phase relationship — they must be coherent. Two independent light bulbs never interfere visibly because their phases jitter randomly billions of times a second, smearing the fringes into uniform gray. This is exactly why interference experiments split one source in two (Young's double slit, an interferometer) rather than using two separate ones.

Interference in space gives fringes; interference in time between two slightly different frequencies gives Beats. Both are the same addition rule, read along different axes.

See also

Related topics

  • BeatsTwo tones of nearly equal frequency drift in and out of step, producing a slow throb whose rate is the difference of the two frequencies.
  • Superposition PrincipleWhen two waves meet, the medium's displacement is simply the sum of what each wave would do alone — the linearity that underlies all of wave physics.
  • WavesFrom a single swinging oscillator to ripples that travel, interfere, and carry frequency through space — the bridge between Oscillations and Fourier Analysis.
  • Standing WaveTrap a wave between two fixed ends and it stops traveling — freezing into a pattern of motionless nodes and violently swinging antinodes.
  • WaveA disturbance that travels through a medium while each point of the medium merely oscillates in place — carrying energy without carrying matter.
  • Doppler EffectMotion of the source or observer compresses the wavefronts ahead and stretches them behind, raising the frequency you receive as it approaches and lowering it as it recedes.

Referenced by