Rope
Flick one end. Watch the pulse travel. The rope goes back.
Slinky
Push and pull. A compression travels down — the coils stay.
Water ripple
Drop a stone. The ripple spreads — the water bobs in place.
In every case you just watched, something moved from one place to another — but if you look carefully, the medium itself (the rope, the coil, the water) did not travel with it.
The rope goes back to rest. The water molecules bob up and down. The Slinky coils compress and expand around the same spot.
What travelled? A disturbance. And with it — something invisible but real: energy.
Why it feels right: waves at the beach look like they're pushing water. But this is a visual illusion — the wave shape (the disturbance) moves, not the bulk water. Surfers ride the moving disturbance, not a current of water.
Why it matters: if air molecules flew to your ears, breathing would be impossible in a noisy room. The energy of sound arrives — the matter (air) does not.
The equation shows it: v = fλ. If v is fixed and f increases, λ must decrease proportionally. Speed stays constant for a given medium.
Think of a crowd doing "the wave" in a stadium. Each person stands up and sits back down — they don't move along the row. But the wave shape travels around the stadium. The disturbance travels. The people (the medium) stay put.
This is not a metaphor — it is exactly what happens in every wave: light, sound, seismic waves, water waves. Energy propagates as a pattern through the medium. The medium oscillates about a fixed point.
Once this is clear, everything else in this topic is answering one question: how does the medium oscillate — and how fast does the pattern travel?
Transverse vs longitudinal — just two different ways the medium can oscillate relative to the direction of energy travel.
Amplitude, wavelength, frequency — ways of measuring and describing the oscillation pattern.
v = fλ — a consequence of how many oscillations occur per second and how far apart they are.
Wave speed depends on medium — because the speed is how fast the disturbance propagates through the material, which depends on the material's properties.
Label the diagram: trace from crest to trough, measure the amplitude from the centre line, find one full wavelength.
Crest (peak) — top of the wave.
Trough — bottom of the wave.
Amplitude (A) — height from centre to peak. Bigger A = more energy.
Wavelength (λ) — distance of one full cycle.
Frequency (f) — cycles per second.
Period (T) — time for one cycle. T = 1/f.
If f doubles and v stays constant → λ halves.
Amplitude is not in the wave speed equation — it is independent of speed, frequency, and wavelength.
| Quantity | Symbol | Unit | Measures… |
|---|---|---|---|
| Amplitude | A | m | Max displacement from rest — related to energy |
| Wavelength | λ (lambda) | m | Length of one complete cycle |
| Frequency | f | Hz | Cycles per second |
| Period | T | s | Time for one cycle — T = 1/f |
| Wave speed | v | m/s | Speed of the wave pattern — v = fλ |
Particles oscillate vertically. Wave energy travels horizontally.
Particles vibrate perpendicular (⊥) to the direction of wave propagation.
Features: crests and troughs.
Can be polarised (vibration restricted to one plane).
Examples: light, all EM waves, seismic S-waves, water surface waves, rope waves.
A transverse wave can be modelled as a sine curve:
y = displacement at time t
A = amplitude, f = frequency
Because the vibration is perpendicular to propagation, it can point in any direction in the plane at right angles to travel. A polarising filter restricts the vibration to just one direction — this only works for transverse waves.
This is why polarised sunglasses reduce glare from reflected light (light is transverse) — but there is no such thing as a "polarised sound" (sound is longitudinal).
Dense regions = compressions. Sparse regions = rarefactions.
Particles vibrate parallel (∥) to the direction of wave propagation.
Features: compressions and rarefactions.
Cannot be polarised — vibration has only one possible direction.
Require a material medium — cannot travel through vacuum.
Examples: sound waves, seismic P-waves, Slinky compressions.
Wavelength λ = distance between two successive compressions (or rarefactions).
Speed of sound in air ≈ 340 m/s at 20°C
Key features
- Vibration ⊥ to propagation
- Crests and troughs
- Can be polarised
- EM waves travel in vacuum
- Examples: light, S-waves, water
Key features
- Vibration ∥ to propagation
- Compressions and rarefactions
- Cannot be polarised
- Needs a material medium
- Examples: sound, P-waves
Imagine you stand at a fixed point watching waves pass. In one second, exactly f complete waves go by (that's what frequency means).
Each wave is λ metres long. So in one second, the wave has covered a total distance of f × λ metres.
But distance covered per second is speed — so:
Rearranging: f = v / λ and λ = v / f
λ = v / f = 340 / 440 = 0.773 m
Worked example 2: Light has wavelength 500 nm (5×10⁻⁷ m) and speed 3×10⁸ m/s — find its frequency.
f = v / λ = 3×10⁸ / 5×10⁻⁷ = 6×10¹⁴ Hz
Waves are one of the two fundamental mechanisms by which energy travels (the other is particles). Amplitude is the key link: doubling amplitude quadruples the energy transported per second. This is why a loud sound (large amplitude) carries more energy than a quiet one — and why ocean waves in a storm are so destructive.
Light is a transverse electromagnetic wave. The laws of reflection (angle of incidence = angle of reflection) and refraction (Snell's Law, n = sin i / sin r) arise because light is a wave that slows down in denser media. When it slows, its wavelength changes — but its frequency stays the same. Total internal reflection, lenses, and fibre optics all follow from wave properties.
Sound is a longitudinal pressure wave. Pitch corresponds to frequency. Loudness corresponds to amplitude. The speed of sound depends on the medium: faster in solids (particles closer together), slower in gases. Echoes, sonar, ultrasound scanning — all applications of sound as a wave.
Changing electric and magnetic fields create each other — and propagate as transverse electromagnetic waves. This is why light needs no medium. The entire EM spectrum (radio, microwave, IR, visible, UV, X-ray, gamma) is one family of transverse waves differing only in frequency. Understanding waves is the gateway to understanding all of electromagnetism.
• A wave is a disturbance that travels through a medium (or space). (1)
• Waves transfer energy but NOT matter — the medium oscillates about a fixed position. (1)
(a) Amplitude — maximum displacement of a particle from its rest/equilibrium position; unit: metres (m). (1)
(b) Wavelength — distance between two consecutive identical points on a wave (e.g. crest to crest); unit: metres (m). (1)
(c) Frequency — number of complete wave cycles passing a fixed point per second; unit: hertz (Hz). (1)
• Correct equation: v = f × λ (1)
• Correct substitution: v = 2.5 × 0.4 (1)
• Correct answer: v = 1.0 m/s with unit (1)
• Transverse: oscillation/vibration perpendicular/at right angles to direction of propagation. (1)
• Longitudinal: oscillation/vibration parallel to direction of propagation. (1)
• Example transverse (any one of): EM waves/light/water waves/seismic S-waves. (1)
• Example longitudinal (any one of): sound/seismic P-waves. (1)
• Compression = region where particles are pushed together / high pressure zone; rarefaction = region where particles are spread apart / low pressure zone. (1)
• f = v / λ (1)
• f = 3.0 × 10⁸ / 5.2 × 10⁻⁷ (1)
• f = 5.77 × 10¹⁴ Hz (allow 5.8 × 10¹⁴ Hz) with correct unit (1)
• S-waves are transverse waves. (1)
• Transverse waves can only travel through solids (not liquids or gases). (1)
• Therefore the outer core must be in a liquid state / molten. (1)