When two waves meet they can add up into something bigger or cancel into nothing. That single idea explains soap-bubble colors, the shimmer on a CD, and the most famous experiment in physics. Everything here moves — play with it.
A wave is a travelling disturbance that carries energy from one place to another without carrying the stuff it travels through along with it. Drop a pebble in a pond: the ripple races outward, but the water itself just bobs up and down in place — only the pattern moves.
Drag the sliders below to shape a wave, and watch it travel. Every wave, whether it's water, sound, or light, is described by the same handful of numbers.
The maximum distance the wave pushes away from the rest position — the height of a crest (the top) or the depth of a trough (the bottom). Bigger amplitude means more energy: a tall water wave or a loud sound.
The length of one complete wave — the distance from one crest to the next (or any point to the matching point one cycle later). Measured in metres. For visible light it's astonishingly small, a few hundred-thousandths of a millimetre, and the wavelength is what your eye reads as colour.
Frequency is how many complete waves pass a point each second, measured in hertz (Hz). Period is the time for one complete wave, T = 1/f. A high-frequency wave wiggles rapidly; a low-frequency one lazily.
How fast a crest travels. It ties the other quantities together: v = f λ. In a given material the speed is usually fixed, so squeezing the wavelength shorter forces the frequency higher, and vice-versa.
Waves come in two flavours. In a transverse wave the wiggle is sideways to the direction of travel (light, and the wave drawn above). In a longitudinal wave the wiggle is back-and-forth along the travel direction (sound). The ideas in this tutorial work for both.
Here is the one rule that makes everything else work. If two waves pass through the same point at the same time, the total displacement is just the sum of what each wave would do on its own. This is called the principle of superposition.
Below, the blue wave and the magenta wave overlap, and the coral wave is their sum. Slide the phase to shift one wave relative to the other and watch the sum swell up or collapse to nothing.
Phase says where a wave is in its cycle right now — at a crest, at a trough, or somewhere between. Two waves are in phase when their crests line up, and out of phase when one's crest meets the other's trough. Phase difference measures this mismatch as an angle: 0° (or 360°) is perfectly in phase, 180° is perfectly opposite.
Crests meet crests (in phase). The waves reinforce; the combined amplitude is large.
A crest meets a trough (out of phase). The waves cancel; the combined amplitude is small or zero.
Energy isn't destroyed when waves cancel — it just gets redistributed. Where two waves cancel, extra energy shows up somewhere else where they reinforce. That bookkeeping is exactly what produces the patterns of bright and dark you'll see next.
Two overlapping waves add point-by-point. Line up the crests → big. Crest-on-trough → gone.
Now let two sources make waves at once — like two fingers tapping a pond in rhythm. Their ripples overlap everywhere, and superposition decides the result at each point. The fixed pattern of reinforcing and cancelling that appears is called an interference pattern.
This is a ripple tank seen from above. The bright, strongly-rippling bands are where the two waves add up (constructive); the calm grey bands between them are where they cancel (destructive). Change the spacing and wavelength and watch the bands fan out.
The result of two or more waves overlapping: their displacements add by superposition, producing a fixed pattern of high-amplitude and low-amplitude regions. Constructive interference is where they reinforce; destructive interference is where they cancel.
For a steady, sharp pattern, the two sources must keep a constant phase relationship — they must be coherent. If their phases drift randomly the bright and dark bands wash out. This is why interference experiments use a single light source split into two, rather than two separate bulbs.
Pick any point in the pattern. The two waves had to travel slightly different distances to reach it; that gap is the path difference Δ. Whether the point is bright or dark depends only on how Δ compares to the wavelength:
Δ = 0, λ, 2λ, 3λ … → constructive (bright)
Δ = ½λ, 1½λ, 2½λ … → destructive (dark)
In words: if one wave is a whole number of wavelengths behind the other, they arrive in step and reinforce. If it's behind by a half-wavelength (or any odd number of halves), they arrive opposed and cancel.
Bright = path difference is a whole number of wavelengths. Dark = a half-wavelength off.
In 1801 Thomas Young shone light through two narrow slits and caught it on a screen. If light were simply tiny bullets you'd expect two bright lines. Instead he saw a whole row of evenly-spaced bright and dark fringes — the unmistakable signature of interference. This is the experiment that proved light behaves as a wave.
The two slits act as two coherent sources (Step 3). Light spreads from each, the two paths to any point on the screen differ slightly, and the path-difference rule paints bright and dark bands. Change the setup and watch the fringes respond.
Each bright band on the screen is a fringe; the dark gaps are dark fringes. The centre-to-centre distance between neighbouring bright fringes is the fringe spacing w. For two slits a distance d apart, light of wavelength λ, and a screen a distance L away:
w = λL / d
Bright fringes sit where the path difference is a whole number of wavelengths, d sinθ = mλ (m = 0, 1, 2…); dark fringes where it's a half-integer.
Why this is such a big deal: tiny bullets could never make alternating dark bands — two streams of bullets just pile up in two spots. Only waves, which can cancel, can leave a spot dark by adding more light to it. The fringes are proof that light interferes, and they let us measure the wavelength of light with a ruler: rearrange to λ = w·d / L.
Two slits → a row of fringes. Spacing w = λL/d. Bigger d, tighter fringes.
Diffraction is the spreading of a wave as it passes through an opening or around an obstacle. A wave doesn't march in a perfectly straight beam — at an edge it bends and fans out into the "shadow." The narrower the gap compared with the wavelength, the more dramatically the wave spreads.
Watch straight wavefronts arrive at a slit. After squeezing through, they bow outward into circular ripples, as if the slit itself were a new source. Make the slit narrow and the spreading becomes huge.
Send that spread onto a screen and it isn't a clean blob — it's a bright central band flanked by dimmer bands, separated by dark gaps. This is the single-slit diffraction pattern.
The bending and spreading of waves at an opening or edge. It happens for all waves; it becomes obvious when the opening is roughly the size of the wavelength or smaller. It's why you can hear someone around a corner (sound's wavelength is large) but can't see them (light's wavelength is tiny).
The dark bands of a single slit of width a fall where a·sinθ = mλ for m = 1, 2, 3… (note: this is the condition for dark, the opposite of the double-slit bright condition). The central bright band, between the first dark fringe on each side, is twice as wide as the others — and it holds most of the light's energy.
Diffraction and interference are really the same physics. Diffraction is what you get when you add up the waves from every point across a single opening (a continuous version of Step 3), while the double-slit fringes come from two openings. Real experiments show both at once: double-slit fringes sitting inside a broad single-slit envelope.
Narrow the gap, widen the spread. Diffraction is interference from one opening.
These aren't lab curiosities — interference and diffraction are painting the world around you all the time. Once you know the signature (rainbow colours from things that have no pigment, or patterns of light and dark), you start spotting it everywhere.
Whenever you see colour with no pigment, or a pattern of bright and dark with no obvious cause, suspect waves adding and cancelling. The same superposition rule runs through all of it — from a ripple in a pond to the colour of a hummingbird's throat.
The whole chain of ideas, in order:
| Term | Meaning |
|---|---|
| Wave | a travelling disturbance that carries energy, not matter |
| Amplitude | maximum displacement from rest (height of a crest) |
| Crest / trough | the highest / lowest point of a wave |
| Wavelength (λ) | length of one full wave, crest to crest |
| Frequency (f) | waves passing a point per second, in hertz |
| Period (T) | time for one full wave, T = 1/f |
| Wave speed (v) | speed of a crest, v = f λ |
| Wavefront | a line joining points of a wave that are in phase (e.g. a crest) |
| Phase | where a wave is in its cycle, as an angle |
| In / out of phase | crests aligned (0°) / crest meets trough (180°) |
| Superposition | overlapping waves add their displacements |
| Interference | the fixed pattern from overlapping coherent waves |
| Constructive | waves reinforce → large amplitude (bright) |
| Destructive | waves cancel → small amplitude (dark) |
| Coherent | keeping a constant phase relationship |
| Path difference (Δ) | extra distance one wave travels vs the other |
| Fringe | a bright (or dark) band in an interference pattern |
| Fringe spacing (w) | gap between bright fringes, w = λL/d |
| Diffraction | spreading of a wave through a gap or around an edge |
| Diffraction grating | many slits that split light into its colours |
| Monochromatic | light of a single wavelength (one colour) |