The big idea: There are two simple ways to draw a wave.
A wavefront is a line (or surface) joining points that are all at the same point in their cycle — for example, all the crests.
A ray is a single line that shows the direction the wave is travelling. It is always drawn at right angles to the wavefronts.
New word — phase: Phase means where a point is in its cycle — going up, at a crest, going down, at a trough.
Points in phase are doing exactly the same thing at the same time (e.g. two crests). A wavefront joins points that are all in phase.
Two pictures of the same wave: Wavefronts = the crests, drawn as parallel lines · ray = an arrow pointing the way the wave goes, perpendicular to those lines.
For a wave spreading out from a point the wavefronts are circles; far away they look like straight, parallel lines (plane wavefronts).
The gap between two neighbouring wavefronts (crest to next crest) is exactly one wavelength λ. So the wavefront picture and the wave equation are the same idea seen two ways — the wave equation is given in the data booklet.
- wave speed — how fast the wavefronts move (m s⁻¹)
- frequency — wavefronts passing each second (Hz)
- wavelength — the gap between neighbouring wavefronts (m)
What each letter is on the picture: λ = the distance between two neighbouring wavefronts.
f = how many wavefronts pass a fixed point each second.
v = how fast the wavefronts move along the ray.
[Diagram: phys-formula-triangle] - Available in full study mode
Worked example — speed from the wavefront spacing
Plane wavefronts on water are 0.50 m apart, and 3.0 of them pass a post each second. Find the speed of the wave.
Solution
- The wavefront spacing is the wavelength (λ = 0.50 m) and the wavefronts-per-second is the frequency (f = 3.0 Hz). Start with the given formula:
- Put in the numbers:
- Work it out — keep the unit:
Final answer
wave speed v = 1.5 m s⁻¹.
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How this is tested: Wavefronts and rays are mostly a representation you must read and draw.
- Paper 1A: identify which line is a wavefront and which is a ray, and that the ray is perpendicular to the wavefronts. - Paper 1B / Paper 2: measure the wavelength from the wavefront spacing, then feed it into v = fλ. The same picture reappears in refraction (the wavefronts bend at a boundary).
Classic trap: the ray is NOT along a wavefront — it crosses them at 90°, pointing the way the wave travels.
Measuring λ off the picture: The wavelength is the gap between two neighbouring wavefronts, not the distance across several of them.
If the wavefronts sit at 2 m and 5 m, then λ = 5 − 2 = 3 m.
IB-style question — speed from a wavefront diagram
A snapshot of a sound wave shows straight, parallel wavefronts. Neighbouring wavefronts are 3.0 m apart, and the source vibrates at 110 Hz. Find the speed of the sound.
Solution
- The wavefront spacing is the wavelength (λ = 3.0 m) and the source frequency is f = 110 Hz. Start with the given formula:
- Put in the numbers:
- Work it out — keep the unit:
Final answer
speed of sound v = 330 m s⁻¹ — a sensible value for sound in air.