IB Physics SLTopic C.3 — How Waves BehavePaper 1 & 2Wavefronts ⟂ rays~6 min read
Wavefronts & Rays
Before we can talk about waves bending, bouncing and overlapping, we need two simple ways of drawing them. Wavefronts capture the shape of a wave; rays capture the direction it’s heading. Get these straight and every later diagram falls into place.
📘 What you need to know
A surface wave travels in two dimensions and has circular wavefronts (like ripples on water)
A spherical wave travels in three dimensions and has spherical wavefronts (like sound or light)
A wavefront joins all the points of a wave that are oscillating in phase
A ray is an arrow showing the direction of travel (and energy transfer)
Rays are always perpendicular (90°) to the wavefronts
The distance between two successive wavefronts equals one wavelengthλ
Waves in Two and Three Dimensions
Drop a stone in a pond and the ripples spread out as growing circles — that’s a surface wave, travelling in two dimensions with circular wavefronts. Sound and light instead spread out in every direction through space as growing spheres — spherical wavefronts in three dimensions. (A spherical wavefront of radius r spreads its energy over a sphere’s surface area, A = 4πr², which matters later when we look at intensity.)
A surface wave from a point source: circular wavefronts (teal = crest, dashed = trough) spread outward, with rays (grey) pointing radially outward at 90° to them. Successive wavefronts are one wavelength apart.
Wavefronts
A wavefront is a line joining all the points of a wave that are oscillating in phase — all at a crest together, say, or all at a trough together. Because those points move in step, the wavefront marks the “leading edge” of one part of the wave. Each wavefront is one wavelength behind the last.
Rays
A ray is simply an arrow showing the direction the wave is travelling (and carrying its energy). The key rule to remember: a ray is always drawn perpendicular — at 90° — to the wavefronts. Viewed from above, a flat wave’s wavefronts look like a series of parallel straight lines, and the ray cuts straight across them.
Viewed from above, wavefronts are parallel lines and the ray runs perpendicular to them. The wavelength λ is the gap between two successive crest wavefronts.
Reading Wavefront Diagrams
In exam diagrams, crest wavefronts are usually drawn as darker solid lines and troughs as fainter or dashed lines — though some diagrams show only the crests. Whichever is used, the rule for measuring is the same: the distance between two successive crest wavefronts (or two successive trough wavefronts) is exactly one wavelength.
🧭 Sketching and reading wavefronts
Draw wavefronts as straight, evenly spaced lines with a ruler — sloppy sketches lose marks
Keep the spacing equal to one wavelength between successive crests
Add the ray as an arrow at exactly 90° to the wavefronts
To find λ from a diagram, measure between two successive crest (or trough) wavefronts
Circular wavefronts ⇒ 2D surface wave; spherical wavefronts ⇒ 3D wave like sound or light
Quick recap: wavefronts join points in phase and sit one wavelength apart; rays point the way the wave travels, always at 90° to the wavefronts.
WE 1
On a wavefront diagram, six successive crest wavefronts are spread evenly over a distance of 10 cm. The wave travels at 3.0 m s⁻¹.
(a) Determine the wavelength. (b) Hence find the frequency.
Part (a)
Six wavefronts make five equal gaps, so λ = 10 cm ÷ 5
λ = 2.0 cm = 0.020 mλ = 0.020 mPart (b)
Using v = fλ, so f = v/λ
f = 3.0 ÷ 0.020f = 150 HzCareful: six wavefronts means five gaps, not six — a classic counting slip.
WE 2
A small loudspeaker emits sound equally in all directions.
(a) State the shape of its wavefronts. (b) State how a ray is drawn relative to these wavefronts.
Part (a)
Sound spreads in three dimensions, so the wavefronts are sphericalPart (b)
A ray points radially outward from the speaker, perpendicular (90°) to each wavefront
Circular wavefronts would be for a 2D surface wave; sound in open air is 3D, hence spherical.
💡 Top tips
Rays and wavefronts are always at 90° — draw the right angle clearly
Circular = 2D (a circle), spherical = 3D (a sphere) — don’t mix the two up
The gap between successive crest wavefronts is one wavelength, so count gaps, not lines
Use a ruler for wavefront and ray diagrams; examiners reward neat, straight lines
Points on the same wavefront are in phase with each other
⚠ Common mistakes
Confusing circular (2D) with spherical (3D) wavefronts
Drawing the ray along the wavefront instead of perpendicular to it
Counting wavefronts instead of the gaps between them when measuring wavelength
Uneven or freehand wavefront spacing — they should be equal and ruler-straight
Thinking a ray shows the wave’s shape; it only shows its direction
Up next: now that we can draw waves, we watch what happens when they hit a boundary — Reflection, Refraction & Transmission.
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