Diffraction and Interference

Two of the most wave-like things waves do

Some behaviours show up only in waves — never in solid particles flying in straight lines. Two of the most striking are diffraction (waves bending around obstacles) and interference (waves adding and cancelling). Together they are the fingerprints that let physicists prove something is a wave. If wavelength and frequency are familiar, you are ready.

Diffraction: waves that bend around edges

When a wave passes through a gap or sweeps past the edge of an obstacle, it does not stay in a tidy beam — it spreads out. This spreading is diffraction.

How much a wave diffracts depends on the size of the gap compared with its wavelength:

• Gap much wider than the wavelength → the wave passes almost straight through with only slight spreading at the edges.
• Gap about the same size as the wavelength → maximum spreading; the wave fans out in a wide arc.
• Gap much smaller than the wavelength → very little gets through.

This is why you can hear someone talking from around a corner. Sound waves are about a metre long, similar to a doorway, so they diffract generously and fill the next room. Light waves are hundreds of thousands of times shorter, so they barely bend and cast sharp shadows instead.

Superposition: waves that pass through each other

Unlike two balls, two waves can occupy the same place at the same moment. When they do, their displacements simply add together. This rule is called superposition. A moment later each wave continues on its way unchanged, as if the other had never been there.

Interference: adding and cancelling

When two waves overlap, superposition produces interference, which comes in two kinds.

Constructive interference happens when the waves are in step — crest lined up with crest, trough with trough. They reinforce each other into a wave with a bigger amplitude. Two equal waves make one twice as tall.

Destructive interference happens when the waves are out of step — a crest of one lands on a trough of the other. They cancel. If the two are equal in size, the result is nothing at all: silence, darkness, or flat water.

Whether you get reinforcement or cancellation depends on the path difference — how much farther one wave has travelled than the other. A whole number of wavelengths of difference gives constructive interference; a half-wavelength difference gives destructive.

The double-slit experiment

In 1801 Thomas Young shone light through two narrow, closely spaced slits onto a screen. If light were just tiny bullets you would expect two bright stripes behind the slits. Instead he saw many bright and dark bands marching across the screen.

The explanation is interference. Light diffracts out from each slit, and the two spreading waves overlap. Where crests meet crests you get a bright band (constructive); where a crest meets a trough you get a dark band (destructive). Particles cannot do this — only waves can. Young's experiment was powerful evidence that light is a wave, and a version of it remains central to modern physics.

Worked example: bright or dark?

Two loudspeakers play the same 1700 Hz note in step. Sound travels at 340 m/s, so the wavelength is:

λ = v / f = 340 ÷ 1700 = 0.2 m

You stand where one speaker is exactly 0.1 m farther away than the other. That path difference is half a wavelength (0.2 ÷ 2 = 0.1 m), so a crest from one arrives with a trough from the other.

Path difference = ½ λ → destructive interference → a quiet spot

Step sideways until the path difference becomes a full 0.2 m (one whole wavelength) and the sound swells back to loud — constructive interference. Real rooms have these quiet and loud spots, which is one reason sound engineers position speakers so carefully.

Try it yourself! 🧪

See interference in water.

1. Fill a shallow, light-coloured tray with about 1 cm of water and let it settle.
2. Dip two fingertips into the water at the same instant, a few centimetres apart, tapping gently and steadily in rhythm.
3. Watch where the ripple rings from your two fingers overlap. In some directions the ripples reinforce into tall waves; in others they flatten to near-stillness.
4. The fan of calm and choppy lines you see is an interference pattern — the same pattern, scaled up, that Young saw with light.

Tap slower (longer wavelength) and the spreading and the pattern both widen — a direct demonstration of diffraction and interference working together.