Drop a stone in a pond and you don’t see a sine curve — you see rings, spreading outwards. Every ring is a line of water rising together, all in step. Those rings are wavefronts, and the arrows pointing straight out from the splash are rays. Both draw the same wave; they just answer different questions. This page is the vocabulary you’ll use for the rest of the topic.
📘 What you need to know
A surface wave spreads in two dimensions and has circular wavefronts (a circle is 2D)
A spherical wave spreads in three dimensions and has spherical wavefronts (a sphere is 3D)
A wavefront joins all the points oscillating in phase — e.g. a line of crests
A ray is a line showing the direction of energy transfer
Rays and wavefronts are always perpendicular to each other
The distance between successive crest wavefronts is one wavelength
Waves spread out in 2D and 3D
So far we’ve drawn waves as a single wiggly line. Real waves fill space. How they fill it depends on how many dimensions they can spread into.
A surface wave travels across a surface — ripples on water. It spreads in two dimensions, so its wavefronts are circles growing outwards from the source.
A spherical wave travels through a volume — sound in air, light from a bulb. It spreads in three dimensions, so its wavefronts are spheres growing outwards.
Ripples from a point source. Solid circles are crest wavefronts, faint dashed circles are troughs, and the red rays point straight out — always at 90° to the wavefronts. One wavelength is crest wavefront to crest wavefront.
The words trip people up, so tie them to shapes you already know. A circle is a 2D shape → circular wavefronts are 2D (water). A sphere is a 3D shape → spherical wavefronts are 3D (sound, light). If you can hear it or see it coming from all around you, it’s spherical.
For a spherical wave, each wavefront is the surface of a sphere of radius r, so its area is just the surface area of a sphere:
Area of a spherical wavefrontA = 4πr2
Double the distance from the source and the wavefront’s area becomes four times bigger — the same energy has to cover four times as much surface. That’s why a shout fades so quickly as you walk away from it.
Wavefronts and rays
These are the two standard ways of drawing a wave, and each has a strict definition.
Definition — wavefront
A line joining all the points that oscillate in phase, drawn perpendicular to the direction of energy transfer
“In phase” means every point on the line is doing exactly the same thing at the same moment — all rising to a crest together, or all dipping to a trough together.
Definition — ray
A line showing the direction of motion and energy transfer of the wave, drawn perpendicular to the wavefront
So a ray is an arrow saying “the wave goes this way”, and a wavefront is a line saying “all of this is a crest right now“. Draw one and the other is fixed, because they always meet at 90°.
Side view of the same wave. Wavefronts (vertical lines) sit on the crests and troughs; the ray (red) runs along the travel direction and crosses every wavefront at 90°.
Wavefront points in phase
always at 90° to
Ray an arrow
points along
Energy transfer wave direction
Viewing waves from above
Far from the source, the circles have grown so large that a small patch of them looks straight. We then draw the wave as a row of parallel wavefronts — the view you’d get looking down on a ripple tank.
Two drawing conventions to know:
Crest wavefronts are drawn as darker, solid lines
Trough wavefronts are drawn as fainter lines — and many diagrams leave them out entirely, showing crests only
Plane wavefronts seen from above. The gap between two successive crest wavefronts is one wavelength, and the ray cuts them all at right angles.
Measuring λ from a wavefront diagram: take the distance between two successive crest wavefronts (or two successive troughs). Never crest-to-trough — that’s only half a wavelength.
Wavefronts vs rays
Feature
Wavefront
Ray
What it is
A line of points oscillating in phase
An arrow along the direction of travel
Drawn how
Line (crests solid, troughs faint)
Straight arrowed line
Direction
Perpendicular to the ray
Perpendicular to the wavefront
Tells you
Where the crests are now
Where the energy is going
Spacing means
Gap between crests = λ
Nothing — rays have no spacing rule
✏️ Drawing a wavefront-and-ray diagram
Decide the travel direction and draw the ray as an arrow.
Draw the wavefronts at 90° to that arrow — straight lines for a distant wave, arcs for one near a point source.
Space them equally. The gap is one wavelength, and it must stay constant unless the wave changes medium.
Use a ruler. Sloppy freehand lines lose marks; examiners check the 90° and the equal spacing.
WE 1
A dipper in a ripple tank makes circular wavefronts at 12 Hz. The distance from the 1st crest wavefront to the 6th is 20 cm. Calculate the wavelength and the speed of the waves.
Step 1 — count the gaps, not the lines
From the 1st to the 6th wavefront there are 5 gaps, not 6.
λ = 20 / 5 = 4.0 cm = 0.040 mStep 2 — use the wave equation v = fλv = 12 × 0.040λ = 4.0 cm, v = 0.48 m s⁻¹Dividing by 6 instead of 5 is the classic slip. Six fence posts, five gaps.
WE 2
A small loudspeaker emits spherical wavefronts. Calculate the area of the wavefront that is 3.0 m from the speaker, and state how the area changes at 6.0 m.
Step 1 — a spherical wavefront is the surface of a sphere
A = 4πr²
Step 2 — substitute r = 3.0 mA = 4π × 3.0² = 113 m²Step 3 — at r = 6.0 m the radius is doubledA = 4π × 6.0² = 452 m²113 m², and 4× bigger at 6.0 mDouble the distance, quadruple the area — because r is squared. The same sound energy is spread far more thinly.
WE 3
Plane wavefronts cross a ripple tank at 0.24 m s⁻¹. Successive crest wavefronts are 1.5 cm apart. Calculate the frequency of the waves.
Step 1 — the gap between successive crest wavefronts is λ
λ = 1.5 cm = 0.015 m
Step 2 — rearrange v = fλ for f
f = v / λ
f = 0.24 / 0.015f = 16 HzSixteen crests sweep past any fixed point every second. Convert cm to m first, or you’ll be out by 100.
💡 Top tips
Circle = 2D, sphere = 3D. The shape name gives the dimensions away.
Rays and wavefronts are always perpendicular. If your sketch doesn’t show 90°, it’s wrong.
Count gaps, not lines, when measuring wavelength from a wavefront diagram.
Draw diagrams with a ruler — equal spacing and clean right angles earn the marks.
A ray is not a wave. It’s just an arrow showing which way the energy goes.
⚠ Common mistakes
Thinking a ray is a thin beam of the wave — it is a direction line, nothing more
Drawing wavefronts parallel to the ray instead of perpendicular
Measuring λ from a crest wavefront to a trough wavefront — that’s only λ/2
Counting lines instead of gaps, giving a wavelength that’s slightly too small
Saying a sound wave has circular wavefronts — sound fills 3D space, so they’re spherical
Letting the wavefront spacing drift in a sketch — if the medium doesn’t change, λ doesn’t change
Quick recap: Waves spread in 2D as circular wavefronts and in 3D as spherical ones (area A = 4πr2). A wavefront joins points oscillating in phase; a ray is an arrow along the direction of energy transfer. The two are always perpendicular, and the distance between successive crest wavefronts is one wavelength.
You can now draw any wave two ways — and that’s exactly the toolkit you need for what comes next. Send a ray at a boundary between two materials and interesting things happen: some of it bounces back, some carries on but bends. That’s reflection, refraction and transmission, on the next page, and every diagram in it is built from rays and wavefronts.
Getting to grips with wave diagrams?
Book a free meeting and we’ll practise sketching wavefronts, rays and past-paper wave questions together.
