Transverse and Longitudinal Waves

This lesson introduces the two fundamental types of wave — transverse and longitudinal — as required by the AQA GCSE Combined Science Trilogy specification (8464), Physics Paper 2, section 6.1. Waves transfer energy from one place to another without transferring matter. A secure understanding of these wave types underpins every other topic in the Waves chapter.

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What Is a Wave?

A wave is a disturbance that transfers energy from one place to another. The key principle for your exam is that waves transfer energy, not matter. The particles of the medium oscillate (vibrate) about their rest position but do not travel along with the wave.

Key facts about waves:

• Waves transfer energy without transferring matter.
• Waves can travel through a medium (a material such as air, water or rock) or, in some cases, through a vacuum (empty space).
• The substance through which a wave travels is called the medium.
• When a wave passes through a medium, the particles of the medium vibrate and then return to their original position.

Exam Tip (AQA 8464): A very common exam question asks "What do waves transfer?" The answer is always energy. Never say waves transfer "matter" or "particles." The particles vibrate but stay in roughly the same position.

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Transverse Waves

In a transverse wave, the oscillations (vibrations) of the particles are perpendicular (at right angles) to the direction of energy transfer.

graph LR
    subgraph "Transverse Wave"
    direction LR
    A["Energy transfer →"] --- B["↑ Crest"]
    B --- C["↓ Trough"]
    C --- D["↑ Crest"]
    D --- E["↓ Trough"]
    end

Imagine shaking a rope up and down: the wave travels horizontally along the rope, but the particles of the rope move up and down (vertically). The oscillations are at 90° to the direction the wave moves.

Examples of Transverse Waves

Wave Type	Medium	Notes
Light (all EM waves)	Can travel through a vacuum	Part of the electromagnetic spectrum
Water waves (surface)	Water surface	Particles move up and down
S-waves (seismic)	Solid rock only	Cannot travel through liquids
Waves on a string or rope	String / rope	Classic classroom demonstration

Features of Transverse Waves

• The oscillations are perpendicular to the direction of energy transfer.
• Transverse waves can be polarised (the oscillations are restricted to one plane).
• Transverse waves have peaks (crests) and troughs.
• All electromagnetic waves are transverse.

Exam Tip: If asked to identify whether a wave is transverse, look for the keyword perpendicular. Draw a double-headed arrow for oscillation direction and a single arrow for the direction of energy transfer in your diagram.

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Longitudinal Waves

In a longitudinal wave, the oscillations of the particles are parallel to the direction of energy transfer. The particles vibrate back and forth in the same direction the wave is moving.

graph LR
    subgraph "Longitudinal Wave"
    direction LR
    A["|||| Compression"] --- B["  |  |  |  Rarefaction"]
    B --- C["|||| Compression"]
    C --- D["  |  |  |  Rarefaction"]
    end

Imagine pushing and pulling a slinky spring horizontally: the coils bunch together (compressions) and spread apart (rarefactions) as the wave travels along.

Examples of Longitudinal Waves

Wave Type	Medium	Notes
Sound waves	Solids, liquids, gases	Cannot travel through a vacuum
Ultrasound	Solids, liquids, gases	Frequency above 20 000 Hz
P-waves (seismic)	Solids and liquids	Faster than S-waves
Waves in a slinky spring	Spring	Compressions and rarefactions visible

Compressions and Rarefactions

Longitudinal waves consist of alternating regions of:

• Compression — where particles are pushed close together (high pressure).
• Rarefaction — where particles are spread far apart (low pressure).

Exam Tip: In longitudinal waves, the wavelength is measured from the centre of one compression to the centre of the next compression (or from one rarefaction to the next). Do not confuse compressions with peaks — peaks and troughs only apply to transverse waves.

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Comparing Transverse and Longitudinal Waves

Feature	Transverse Wave	Longitudinal Wave
Oscillation direction	Perpendicular to energy transfer	Parallel to energy transfer
Examples	Light, water waves, S-waves	Sound, ultrasound, P-waves
Features	Peaks (crests) and troughs	Compressions and rarefactions
Can be polarised?	Yes	No
Can travel through a vacuum?	Some (EM waves)	No
Need a medium?	EM waves do not; others do	Always need a medium

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Mechanical and Electromagnetic Waves

Waves can also be classified as mechanical or electromagnetic:

• Mechanical waves require a medium to travel through. They cannot travel through a vacuum. Examples: sound waves, water waves, seismic waves.
• Electromagnetic (EM) waves do not require a medium. They can travel through a vacuum (empty space). All EM waves are transverse. Examples: light, radio waves, X-rays.

graph TD
    W["Waves"] --> M["Mechanical Waves"]
    W --> E["Electromagnetic Waves"]
    M --> MT["Can be transverse or longitudinal"]
    M --> MR["Require a medium"]
    E --> ET["Always transverse"]
    E --> ER["Can travel through a vacuum"]

    style W fill:#2c3e50,color:#fff
    style M fill:#2980b9,color:#fff
    style E fill:#e74c3c,color:#fff
    style MT fill:#3498db,color:#fff
    style MR fill:#3498db,color:#fff
    style ET fill:#c0392b,color:#fff
    style ER fill:#c0392b,color:#fff

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Demonstrating Transverse and Longitudinal Waves

In the classroom, you can demonstrate both types of wave:

Demonstration	Wave type	What to observe
Shaking a rope / slinky sideways	Transverse	Crests and troughs travel along the rope while each point moves up and down
Pushing and pulling a slinky along its length	Longitudinal	Compressions and rarefactions travel along the spring while each coil moves back and forth
Ripple tank with a straight dipper	Transverse (surface water waves)	Wavefronts travel outward; water particles move up and down

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Common Mistakes

Mistake	Correction
"Waves transfer particles from place to place"	Waves transfer energy, not particles
"Sound is a transverse wave"	Sound is a longitudinal wave
"All waves need a medium"	EM waves can travel through a vacuum
"Wavelength in longitudinal waves is crest to crest"	Use compression to compression for longitudinal waves
Confusing perpendicular and parallel	Transverse = perpendicular; Longitudinal = parallel

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Summary

• A wave transfers energy without transferring matter.
• In a transverse wave, oscillations are perpendicular to the direction of energy transfer (e.g. light, water waves).
• In a longitudinal wave, oscillations are parallel to the direction of energy transfer (e.g. sound).
• Longitudinal waves have compressions and rarefactions; transverse waves have crests and troughs.
• Mechanical waves need a medium; electromagnetic waves can travel through a vacuum.
• Only transverse waves can be polarised.
• The AQA (8464) specification requires you to describe, compare and give examples of both wave types.

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Extended Worked Examples

Although this lesson is mostly about classifying waves, AQA often combines the classification with short quantitative tasks using v = fλ and the period–frequency relationship T = 1/f. Here are four worked examples that reinforce the idea that type (transverse or longitudinal) does not change the underlying equations.

Worked Example 1 — A transverse wave on a rope

A student shakes one end of a long rope up and down 4 times every 2 seconds. The peaks are 0.5 m apart. Calculate the frequency and wave speed.

• Frequency: 4 complete oscillations in 2 s, so f = 4 / 2 = 2 Hz.
• Wavelength: λ = 0.5 m (peak to peak — remember: distance between equivalent points).
• Wave speed: v = fλ = 2 × 0.5 = 1.0 m/s.

The rope itself is a transverse wave because each point on the rope moves vertically while energy travels horizontally.

Worked Example 2 — A longitudinal sound wave

A loudspeaker produces a sound wave with a period of 0.0025 s. The wavelength in air is 1.36 m. Calculate the wave speed.

• Frequency: f = 1 / T = 1 / 0.0025 = 400 Hz.
• Wave speed: v = fλ = 400 × 1.36 = 544 m/s.

This is faster than the standard 340 m/s because the example numbers are not real air conditions — AQA examiners sometimes deliberately give unrealistic numbers to make sure you use the equation rather than recall the "textbook" speed of sound.

Worked Example 3 — Comparing two wave types

Two waves travel at 300 m/s through the same medium. Wave A has a frequency of 150 Hz; wave B has a frequency of 600 Hz.

Wave	Frequency	Wavelength (λ = v ÷ f)
A	150 Hz	300 / 150 = 2.0 m
B	600 Hz	300 / 600 = 0.5 m

Wave B has one quarter the wavelength of wave A because its frequency is four times higher. This reinforces the inverse relationship between frequency and wavelength at constant wave speed — true for both transverse and longitudinal waves.

Worked Example 4 — Compression-to-compression measurement

In a slinky demonstration, a student counts 6 compressions in a 90 cm length of spring. Estimate the wavelength.

• Between 6 compressions there are 5 wavelengths (not 6). So λ = 0.90 ÷ 5 = 0.18 m.

Common-mistake callout: Students frequently divide by the number of compressions rather than the number of gaps between compressions. Always count the gaps — this is the same rule used when measuring the wavelength of ripples in the tank.

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Quick-reference Comparison Table

Question asked by AQA	Transverse answer	Longitudinal answer
What is the direction of oscillation?	Perpendicular to energy transfer	Parallel to energy transfer
What regions/features does it have?	Crests and troughs	Compressions and rarefactions
Can it be polarised?	Yes	No
Can it travel through a vacuum?	Only EM waves can	No — needs a medium
How is wavelength measured?	Crest to crest (or trough to trough)	Compression to compression
Typical GCSE example	Water ripples, light	Sound, P-waves
What does large amplitude mean?	Brighter light / bigger swell	Louder sound

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Diagram: Energy Transfer without Matter Transfer

graph LR
    subgraph "Energy transfers — matter stays put"
    direction LR
    P1["Particle 1 oscillates"] -.->|"passes energy"| P2["Particle 2 oscillates"]
    P2 -.->|"passes energy"| P3["Particle 3 oscillates"]
    P3 -.->|"passes energy"| P4["Particle 4 oscillates"]
    end
    style P1 fill:#2980b9,color:#fff
    style P2 fill:#2980b9,color:#fff
    style P3 fill:#2980b9,color:#fff
    style P4 fill:#2980b9,color:#fff

Each particle returns to its equilibrium (rest) position. Only the energy travels through the medium. This applies equally to transverse and longitudinal waves.

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Mini Quiz (AQA-style)

1. State, with a reason, whether sound is a transverse or longitudinal wave. (2 marks)
2. Define "amplitude" using precise physics vocabulary. (1 mark)
3. Explain why sound cannot travel through a vacuum. (2 marks)
4. A transverse wave on water has a wavelength of 0.4 m and a frequency of 5 Hz. Calculate the wave speed. (2 marks)

Suggested answers:

1. Longitudinal; the oscillations of air particles are parallel to the direction of energy transfer, forming compressions and rarefactions.
2. The maximum displacement of a point on the wave from its undisturbed (equilibrium) position.
3. A vacuum contains no particles; longitudinal waves require particles to form compressions and rarefactions, so there is no medium to carry the energy.
4. v = fλ = 5 × 0.4 = 2.0 m/s.

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Answering at different grade levels

How deeply you explain the ideas of transverse vs longitudinal waves is a key driver of your grade in AQA Paper 2.

• Grade 3–4 response: "Transverse waves go up and down, longitudinal waves go back and forth. Sound is longitudinal and light is transverse." This scores the basic recall mark but misses the precise vocabulary.
• Grade 5–6 response: Uses precise terms — perpendicular and parallel to the direction of energy transfer — and gives correct examples (water, light, S-waves vs sound, P-waves, ultrasound). Mentions amplitude correctly as maximum displacement from rest.
• Grade 7–9 response: Links wave type to observable properties. For example: "Transverse waves can be polarised because the oscillations can be restricted to a single plane; longitudinal waves cannot. All electromagnetic waves are transverse and travel at 3 × 10⁸ m/s in a vacuum. Sound (a longitudinal wave) has a frequency that determines pitch and an amplitude that determines loudness; its period is 1/f." Uses the vocabulary wavelength, frequency, period and amplitude accurately, and explains the particle model that underpins the classification.

AQA alignment: This content is aligned with AQA GCSE Combined Science: Trilogy (8464) specification section 6.6 Waves — specifically 6.6.1.1 Transverse and longitudinal waves and 6.6.1.2 Properties of waves. Assessed on Physics Paper 2.