Wave Properties¶
Syllabus mapping
PY-11-02 — Waves. Covers: classifying waves as transverse or longitudinal; wave terminology (wavelength, amplitude, period, frequency); the wave equation \(v=f\lambda\); displacement–time and displacement–distance graphs; the use of wave velocity/wavelength by Aboriginal and Torres Strait Islander Peoples to estimate water depth (explicit, examinable content integration point).
Wording above is paraphrased for teaching use — cross-check against the official syllabus PDF (see Resources) before treating any line as verbatim NESA text.
You need to know: the difference between transverse and longitudinal waves, the standard wave terminology, how to use \(v=f\lambda\), and how to read a displacement–time graph vs a displacement–distance graph without mixing them up.
Assumed knowledge check¶
Before this page makes sense, you should be comfortable with:
- Graphs — reading line graphs, gradient, period-type patterns
- Algebra — rearranging multi-step equations
Core¶
Waves transfer energy, not matter¶
A wave is a disturbance that transfers energy through a medium (or, for EM waves, through empty space) without any net transport of matter — individual particles in the medium oscillate about a fixed mean position; they don't travel with the wave. A duck floating on water bobs up and down as a ripple passes, but doesn't get carried along with it.
Transverse vs longitudinal waves¶
- Transverse: particle oscillation is perpendicular to the direction of energy transfer. Examples: light and other EM waves, waves on a string, water surface waves.
- Longitudinal: particle oscillation is parallel to the direction of energy transfer — the medium compresses and rarefies. Example: sound.
Wave terminology¶
| Term | Symbol | Meaning |
|---|---|---|
| Wavelength | \(\lambda\) | Distance between successive identical points (e.g. crest to crest) |
| Amplitude | — | Maximum displacement from the equilibrium (undisturbed) position |
| Period | \(T\) | Time for one complete oscillation |
| Frequency | \(f\) | Number of oscillations per second, \(f = \dfrac{1}{T}\) |
The wave equation¶
Worked example
A sound wave has a frequency of \(440\ \text{Hz}\) (the musical note A) and travels at \(340\ \text{m s}^{-1}\) in air (the speed of sound given on your data sheet). Find its wavelength.
Displacement–time vs displacement–distance graphs¶
🖼️ Diagram needed: side-by-side graphs of the same wave. Left panel — displacement–time, x-axis in seconds, with the period \(T\) marked as the horizontal distance between two successive peaks. Right panel — displacement–distance (a "snapshot" at one instant), x-axis in metres, with the wavelength \(\lambda\) marked as the horizontal distance between two successive peaks. Use matching amplitude/shape in both panels so it's visually obvious they're the same wave sliced two different ways, and add a one-line caption under each axis reinforcing what it actually shows ("one point's motion over time" vs "the wave's shape at one instant"). This pair is commonly confused and deserves a clean visual. TODO — placeholder until sourced/drawn.
These look similar but show completely different things:
| Displacement–time graph | Displacement–distance graph | |
|---|---|---|
| Shows | Motion of one point in the medium, over time | The whole wave's shape at one instant (a "snapshot") |
| Horizontal axis | Time | Position/distance |
| Reading period | Time between repeats on this graph | — (not readable here) |
| Reading wavelength | — (not readable here) | Distance between repeats on this graph |
The single most common mix-up: reading a wavelength off a displacement–time graph, or a period off a displacement–distance graph. Neither works — check which quantity is on the horizontal axis before reading anything off it.
Aboriginal and Torres Strait Islander content — placeholder, not yet written
NESA lists the use of wave velocity/wavelength by Aboriginal and Torres Strait Islander Peoples to estimate water depth as explicit, examinable syllabus content — not an optional cultural add-on (see project.md Section 0). The underlying physics principle (wave speed changes as water depth changes, which shows up as a change in wavelength since frequency stays fixed) is real and can be taught accurately, but the specific cultural knowledge and its context needs proper research — ideally with input from your school's Aboriginal Education team or a community-verified source — rather than a generic paraphrase.
Deliberately left unwritten here rather than filled with unverified content — flagging clearly so it doesn't get missed, per the project's own checklist (project.md Section 7, "don't skip as 'extra'").
Advanced
Multi-step wave equation problems — combining \(v=f\lambda\) with \(f = \dfrac{1}{T}\) in the same problem, e.g. given a period and a wave speed, find wavelength; given two of the three (\(v\), \(f\), \(\lambda\)) in inconsistent-looking units, convert before substituting.
Wave speed changing between media. When a wave crosses into a new medium, its frequency stays the same (set by the source), but its speed and wavelength both change together — this is the setup for refraction, covered properly in Wave Behaviours. Worth previewing here: if \(v\) changes and \(f\) doesn't, \(\lambda\) must change to match, directly from \(v=f\lambda\).
Extension
Beyond the Physics 11–12 syllabus — won't appear in the HSC, included for interest / depth study inspiration.
📎 Depth study idea
Real sounds — a musical instrument, a voice — are almost never a single pure sine wave. What we hear as a distinct instrument's tone (its timbre) comes from a superposition of a fundamental frequency plus multiple harmonics (integer multiples of the fundamental) at different amplitudes, added together. This is Fourier decomposition: any periodic waveform, however complex, can be built from a sum of pure sine waves. A depth study could record and analyse the frequency spectrum of a real instrument (many free tools do a Fast Fourier Transform on an audio clip) and compare its harmonic content to a theoretical prediction — genuinely connects straight into Light and Sound below.
Video/visual resources¶
- 🖥️ PhET Simulation — Wave on a String — TODO: confirm current PhET link
- 🎥 Khan Academy — TODO: source a transverse/longitudinal waves explainer. Must be animated — oscillation direction vs energy-transfer direction is very hard to convey in static text or images. Essential.
- 🎥 Physics High — TODO: check for a NSW-syllabus-aligned wave properties video, ideally covering the displacement-time vs displacement-distance graph distinction specifically (see the diagram spec above) — that's the concept students most often mix up on this page.
Check yourself¶
-
A water wave has a wavelength of \(2.5\ \text{m}\) and travels at \(1.5\ \text{m s}^{-1}\). Find its frequency.
Answer
\(f = \dfrac{v}{\lambda} = \dfrac{1.5}{2.5} = 0.6\ \text{Hz}\)
-
Classify each as transverse or longitudinal: (a) sound in air, (b) a wave travelling along a guitar string, (c) light.
Answer
(a) Longitudinal — air compresses and rarefies along the direction of travel.
(b) Transverse — the string moves perpendicular to the wave's direction of travel.
(c) Transverse — the electric and magnetic fields oscillate perpendicular to the direction of travel.
-
A displacement–time graph for a wave shows it completes one full cycle every \(0.02\ \text{s}\). Find the frequency. (Trick question — can you find the wavelength from this graph alone?)
Answer
\(T = 0.02\ \text{s}\), so \(f = \dfrac{1}{T} = \dfrac{1}{0.02} = 50\ \text{Hz}\).
Wavelength cannot be found from a displacement–time graph — it only shows one point's motion over time, not the wave's shape in space. You'd need either a displacement–distance graph, or the wave speed (combined with the frequency you just found) via \(v=f\lambda\).