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This lesson covers the fundamental properties of waves — the two main types, key terminology, and the wave equation — as required by the Edexcel GCSE Physics specification (1PH0), Topic 4: Waves. You need to understand how waves transfer energy, distinguish between transverse and longitudinal waves, and use the wave equation confidently in calculations.
A wave is a disturbance that transfers energy from one place to another without transferring matter. The particles of the medium vibrate about their rest position — they do not travel along with the wave.
Key facts about waves:
Exam Tip: A very common exam question asks "What do waves transfer?" The answer is always energy (and information). Never say that waves transfer matter — this is a key misconception the examiners test.
There are two main types of wave: transverse waves and longitudinal waves. The difference is the direction in which the particles of the medium oscillate relative to the direction of energy transfer.
In a transverse wave, the oscillations (vibrations) of the particles are perpendicular (at right angles) to the direction of energy transfer.
Examples of transverse waves:
In a transverse wave, you can identify peaks (crests) and troughs — the highest and lowest points of the wave.
In a longitudinal wave, the oscillations of the particles are parallel to the direction of energy transfer. The particles vibrate back and forth along the same direction the wave travels.
Examples of longitudinal waves:
In a longitudinal wave, you can identify regions of compression (where particles are pushed close together) and rarefaction (where particles are spread further apart).
Exam Tip: To remember the difference — Transverse = oscillations are aT right angles to direction of travel. Longitudinal = oscillations are aLong the direction of travel.
You must know the following terms and be able to identify them on wave diagrams:
| Term | Definition | Unit |
|---|---|---|
| Amplitude (A) | The maximum displacement of a point on the wave from its rest (equilibrium) position | metres (m) |
| Wavelength (λ) | The distance between two consecutive points in phase (e.g. crest to crest, or trough to trough) | metres (m) |
| Frequency (f) | The number of complete waves passing a point per second | hertz (Hz) |
| Period (T) | The time taken for one complete wave to pass a point | seconds (s) |
| Wave speed (v) | The speed at which the wave moves through the medium | metres per second (m/s) |
T = 1 / f and f = 1 / T
Exam Tip: A very common mistake is to measure amplitude as the distance from peak to trough. This gives you double the amplitude. Always measure from the rest position (the middle line) to the peak.
graph LR
A["Peak (crest)"] -.-> B["← Wavelength (λ) →"]
B -.-> C["Peak (crest)"]
D["Rest position"] -.-> E["↑ Amplitude (A)"]
D -.-> F["↓ Amplitude (A)"]
F -.-> G["Trough"]
style A fill:#2980b9,color:#fff
style C fill:#2980b9,color:#fff
style G fill:#c0392b,color:#fff
style D fill:#27ae60,color:#fff
On a transverse wave diagram:
In a longitudinal wave diagram:
graph LR
A["Compression<br/>(particles close)"] --> B["Rarefaction<br/>(particles spread)"]
B --> C["Compression<br/>(particles close)"]
C --> D["Rarefaction<br/>(particles spread)"]
style A fill:#e74c3c,color:#fff
style B fill:#3498db,color:#fff
style C fill:#e74c3c,color:#fff
style D fill:#3498db,color:#fff
The wave equation links wave speed, frequency, and wavelength:
v = f × λ
Where:
This equation is on the Edexcel Physics equation sheet.
A wave has a frequency of 5 Hz and a wavelength of 2 m. Calculate the wave speed.
v = f × λ
v = 5 × 2
v = 10 m/s
A radio wave travels at 3 × 10⁸ m/s and has a frequency of 100 MHz (100 × 10⁶ Hz). Calculate the wavelength.
λ = v / f
λ = (3 × 10⁸) / (100 × 10⁶)
λ = (3 × 10⁸) / (1 × 10⁸)
λ = 3 m
A wave has a period of 0.02 s. Calculate its frequency.
f = 1 / T
f = 1 / 0.02
f = 50 Hz
A wave has a period of 0.005 s and a wavelength of 1.5 m. Calculate the wave speed.
Step 1: Find the frequency.
f = 1 / T = 1 / 0.005 = 200 Hz
Step 2: Use the wave equation.
v = f × λ = 200 × 1.5
v = 300 m/s
Exam Tip: Always show your working clearly, including rearranging the equation. Write the formula first, then substitute the values, then calculate the answer with the correct unit. If the period is given instead of frequency, convert it first using f = 1/T.
A student measures 4 complete wavelengths of a water wave across a distance of 32 cm. The waves pass a fixed point at a rate of 5 waves per second. Calculate the wave speed in metres per second.
Step 1: Find one wavelength.
λ = total distance / number of wavelengths = 0.32 m / 4 = 0.08 m
Step 2: Identify frequency.
f = 5 Hz
Step 3: Apply v = fλ.
v = 5 × 0.08 = 0.4 m/s
An ocean wave has a period of 4.0 s and travels at 6.0 m/s. Find the wavelength.
Step 1: f = 1 / T = 1 / 4.0 = 0.25 Hz
Step 2: λ = v / f = 6.0 / 0.25 = 24 m
A microwave has frequency 2.45 × 10⁹ Hz and travels at 3.0 × 10⁸ m/s. Find λ.
λ = v / f = (3.0 × 10⁸) / (2.45 × 10⁹) = 0.122 m (about 12 cm)
Exam Tip: Keep numbers in standard form until the final step. Converting prematurely causes rounding errors.
| Feature | Transverse | Longitudinal |
|---|---|---|
| Oscillation direction | Perpendicular to energy transfer | Parallel to energy transfer |
| Features seen | Peaks and troughs | Compressions and rarefactions |
| Requires a medium? | Not always (EM can travel in vacuum) | Yes (always needs particles) |
| Examples | Light, water, S-waves, EM | Sound, P-waves, ultrasound |
| Can be polarised? | Yes | No |
Common Mistake Callout: Students often say that transverse waves "go up and down". This is only true for one example (water on a string). The defining property is that oscillation is perpendicular to the direction of energy transfer — which may be any direction, not only vertical.
flowchart TD
A["Given: two of v, f, λ"] --> B{"Which is unknown?"}
B -- "Unknown: v" --> C["v = f × λ"]
B -- "Unknown: f" --> D["f = v / λ"]
B -- "Unknown: λ" --> E["λ = v / f"]
C --> F["Check units: m/s, Hz, m"]
D --> F
E --> F
F --> G["If period T is given, first<br/>convert using f = 1/T"]
style A fill:#2c3e50,color:#fff
style G fill:#27ae60,color:#fff
Grade 3–4 response (basic): "A transverse wave goes up and down and a longitudinal wave goes side to side. You use v = f × λ." This is vague and uses everyday language.
Grade 5–6 response (secure): "In a transverse wave the oscillations are perpendicular to the direction of energy transfer. In a longitudinal wave the oscillations are parallel. The amplitude is the maximum displacement from rest, the wavelength is the distance between two adjacent points in phase, and the frequency is the number of complete waves per second. The wave equation v = fλ links wave speed to frequency and wavelength."
Grade 7–9 response (exemplary): "A transverse wave has particle oscillations perpendicular to the direction of energy transfer, producing peaks and troughs; electromagnetic waves are transverse and can travel through a vacuum. A longitudinal wave has oscillations parallel to energy transfer, producing compressions and rarefactions; sound is longitudinal and cannot travel through a vacuum because no particles exist to be disturbed. The amplitude measures the maximum displacement from equilibrium (a measure of energy carried); wavelength λ is the distance for one complete cycle; frequency f = 1/T. Using v = fλ, for a wave of fixed speed, doubling the frequency halves the wavelength. Crucially, when a wave refracts across a boundary, frequency stays constant while speed and wavelength change in proportion."
Edexcel alignment: This content is aligned with Edexcel GCSE Physics (1PH0) specification Topic 4 Waves — specifically 4.1 Wave types (transverse and longitudinal), 4.2 Wave properties (amplitude, wavelength, frequency, period), and 4.3 The wave equation (v = f × λ, T = 1/f). Assessed on Paper 2.