Transverse and Longitudinal Waves

This lesson introduces the two main types of wave — transverse and longitudinal — and the key properties used to describe them, as required by the Edexcel GCSE Combined Science specification (1SC0). A secure understanding of wave terminology is essential for every topic that follows in this unit.

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What Is a Wave?

A wave is a disturbance that transfers energy from one place to another without transferring matter. The particles of the medium vibrate about a fixed (equilibrium) position but do not travel with the wave.

Key Principle

• Waves transfer energy, not matter.
• The substance through which a wave travels is called the medium (e.g. air, water, glass).
• Some waves (electromagnetic waves) can travel through a vacuum — they do not need a medium.

Exam Tip: A very common exam question asks what waves transfer. The answer is always energy, never matter or particles.

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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.

Feature	Detail
Oscillation direction	Perpendicular to energy transfer
Can travel through	Solids, liquids and vacuums
Examples	Water surface waves, light and all EM waves, S-waves (seismic), waves on a string

Visualising a Transverse Wave

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

The peaks are called crests and the lowest points are called troughs.

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Longitudinal Waves

In a longitudinal wave the oscillations of the particles are parallel to the direction of energy transfer.

Feature	Detail
Oscillation direction	Parallel to energy transfer
Can travel through	Solids, liquids and gases
Examples	Sound waves, ultrasound, P-waves (seismic)

Compressions and Rarefactions

• Compressions — regions where particles are pushed close together (high pressure).
• Rarefactions — regions where particles are spread apart (low pressure).

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

Exam Tip: Remember the mnemonic: Longitudinal — Like a sLinky pushed and pulled along its length; Transverse — The vibrations go Top-to-bottom (perpendicular).

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Key Wave Properties

All waves — whether transverse or longitudinal — can be described using the same set of properties.

Property	Symbol	Unit	Definition
Amplitude	A	metres (m)	Maximum displacement of a point on the wave from its equilibrium (rest) position
Wavelength	λ (lambda)	metres (m)	Distance between two consecutive points in phase (e.g. crest to crest)
Frequency	f	hertz (Hz)	Number of complete waves passing a point per second
Period	T	seconds (s)	Time taken for one complete wave to pass a point

Amplitude

• The amplitude is measured from the rest position to the crest (or to the trough).
• It is not measured from crest to trough — that distance is twice the amplitude.
• A larger amplitude means the wave carries more energy.

Wavelength

• For a transverse wave, wavelength is the distance from one crest to the next crest (or trough to trough).
• For a longitudinal wave, wavelength is the distance from one compression to the next compression.

Frequency and Period

The relationship between frequency and period is:

$f = \frac{1}{T}$f=T1​

and equivalently:

$T = \frac{1}{f}$T=f1​

Quantity	Symbol	Unit
Frequency	f	Hz (s⁻¹)
Period	T	s

Worked Example 1

A wave has a period of 0.02 s. Calculate its frequency.

$f = \frac{1}{T} = \frac{1}{0.02} = 50 \text{ Hz}$f=T1​=0.021​=50 Hz

Worked Example 2

A radio station broadcasts at a frequency of 200 000 Hz. What is the period of the wave?

$T = \frac{1}{f} = \frac{1}{200\,000} = 5 \times 10^{-6} \text{ s}$T=f1​=2000001​=5×10−6 s

Exam Tip: Make sure you can rearrange f = 1/T for both f and T. These quick calculations often appear as 1-mark questions.

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Comparing Transverse and Longitudinal Waves

Feature	Transverse	Longitudinal
Oscillation direction	Perpendicular to energy transfer	Parallel to energy transfer
Can be polarised?	Yes	No
Can travel through a vacuum?	Only EM waves	No
Examples	Light, water waves, S-waves	Sound, ultrasound, P-waves

Polarisation

Polarisation is the restriction of a transverse wave's oscillations to a single plane. Only transverse waves can be polarised. This is evidence that light is a transverse wave.

• Polaroid filters allow oscillations in only one plane to pass through.
• If two Polaroid filters are placed at right angles (crossed polarisers), no light passes through.

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Reading a Wave Diagram

When you are given a displacement–distance graph (a snapshot of a transverse wave):

1. Amplitude = maximum height above (or depth below) the rest position.
2. Wavelength = horizontal distance between two adjacent crests (or troughs).

When you are given a displacement–time graph (how one point moves over time):

1. Amplitude = maximum displacement from rest.
2. Period = time for one complete oscillation.
3. Frequency = 1 / period.

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Worked Example 3 — Reading a Diagram

A displacement–distance graph shows a wave with crests at 0 m and 0.6 m along the x-axis, and an amplitude of 0.04 m.

• Wavelength = 0.6 − 0.0 = 0.6 m
• Amplitude = 0.04 m

If the wave has a frequency of 5 Hz, calculate its period.

$T = \frac{1}{f} = \frac{1}{5} = 0.2 \text{ s}$T=f1​=51​=0.2 s

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Common Misconceptions

Misconception	Correction
Waves move matter from place to place	Waves transfer energy, not matter
Amplitude is the distance from crest to trough	Amplitude is the distance from the rest position to the crest (half the crest-to-trough distance)
Longitudinal waves don't have a wavelength	They do — measured from compression to compression
Sound is a transverse wave	Sound is a longitudinal wave

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Summary

• Transverse waves have oscillations perpendicular to the direction of energy transfer (e.g. light, water waves).
• Longitudinal waves have oscillations parallel to the direction of energy transfer (e.g. sound).
• Key properties: amplitude (A), wavelength (λ), frequency (f) and period (T).
• Frequency and period are related by $f = \frac{1}{T}$f=T1​.
• Waves transfer energy without transferring matter.
• Only transverse waves can be polarised.

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Deeper Exploration of Wave Properties

The Particle-Wave Picture

A useful mental model is a line of people holding hands. If the person at one end shakes their arm up and down (perpendicular to the line), the disturbance travels along the line as a transverse wave — each person bobs up and down but stays in the same place. If instead the person at the end pushes and pulls along the line, each person squashes against the next and then spreads apart as the disturbance passes — a longitudinal wave of compressions and rarefactions.

Model	Transverse Analogy	Longitudinal Analogy
Slinky	Wiggle side to side	Push and pull along length
Rope	Flick one end vertically	(Not well modelled)
Line of students	Sway left/right	Bump shoulders along the line

Phase and Wavefronts

Two points on a wave are said to be in phase if they are at the same stage of their oscillation — for example, both at a crest or both at a trough — and separated by a whole number of wavelengths. A wavefront is a line or surface joining points that are in phase (like the line of crests on a water wave). Wavefronts are always perpendicular to the direction of energy transfer.

graph LR
    A["Source"] --> B["Wavefront 1 (crest)"]
    B --> C["Wavefront 2 (crest)"]
    C --> D["Wavefront 3 (crest)"]
    D --> E["Energy transfer →"]

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Worked Examples with v = fλ, Period and Frequency

Worked Example 4

A wave on a string has an amplitude of 3 cm, a wavelength of 0.40 m and a frequency of 25 Hz. Calculate the wave speed.

Step 1: Write the wave equation.

$v = f \lambda$v=fλ

Step 2: Substitute — both quantities are already in SI units.

$v = 25 \times 0.40$v=25×0.40

Step 3: Calculate.

$v = 10 \text{ m/s}$v=10 m/s

Note that the amplitude is not needed to find the wave speed. Amplitude affects the energy of the wave, not its speed.

Worked Example 5

A loudspeaker vibrates with a period of 2.0 ms. Calculate its frequency.

Step 1: Convert the period to seconds.

$T = 2.0 \text{ ms} = 2.0 \times 10^{-3} \text{ s}$T=2.0 ms=2.0×10−3 s

Step 2: Use f = 1/T.

$f = \frac{1}{2.0 \times 10^{-3}} = 500 \text{ Hz}$f=2.0×10−31​=500 Hz

Worked Example 6

A pendulum swings with a frequency of 0.50 Hz. How many complete oscillations does it make in 10 seconds?

$T = \frac{1}{f} = \frac{1}{0.50} = 2.0 \text{ s per oscillation}$T=f1​=0.501​=2.0 s per oscillation

$\text{number of oscillations} = \frac{10}{2.0} = 5$number of oscillations=2.010​=5

Exam Tip: Always check whether the question gives you period (in seconds) or frequency (in hertz). Mixing them up is one of the most common calculation mistakes at GCSE.

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Amplitude and Energy

The energy carried by a wave depends on its amplitude. Doubling the amplitude does not double the energy — in fact, the energy carried by a mechanical wave is proportional to the square of the amplitude, so doubling the amplitude carries approximately four times the energy. At GCSE Combined Science you only need to remember the qualitative link: larger amplitude → more energy.

Change in amplitude	Change in energy transferred
Doubled	Much greater (roughly four times)
Halved	Much less (roughly one quarter)

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Common Mistakes and Callouts

Common Mistake: Writing that waves "carry particles" or "move matter from A to B". Particles only oscillate about a fixed position — the wave transfers energy.

Common Mistake: Confusing amplitude with wavelength. Amplitude is a vertical distance (measured from rest position to crest); wavelength is a horizontal distance (measured along the direction of travel).

Common Mistake: Saying sound is a transverse wave because you can "see" it as a squiggle on an oscilloscope. The oscilloscope plots pressure against time — but the actual sound wave in air is longitudinal.

Answering at different grade levels

Grade 3-4 answer: "A transverse wave moves up and down, like a water wave. A longitudinal wave squashes and stretches, like sound. Amplitude is how tall the wave is, and wavelength is how long it is. Frequency is how many waves per second."

Grade 5-6 answer: "In a transverse wave, the particles oscillate perpendicular to the direction of energy transfer (e.g. water waves, electromagnetic waves). In a longitudinal wave, particles oscillate parallel to the direction of energy transfer, forming compressions and rarefactions (e.g. sound). Amplitude is the maximum displacement from the equilibrium position; wavelength (λ) is the distance between two consecutive points in phase; frequency (f) is the number of complete oscillations per second in hertz; period (T) is the time for one complete oscillation, linked by f = 1/T."

Grade 7-9 answer: Builds on the grade 5-6 response by adding precise distinctions: wavefronts are perpendicular to the direction of energy transfer; only transverse waves can be polarised, providing evidence for the transverse nature of light and other members of the electromagnetic spectrum. Points in phase are separated by a whole number of wavelengths and are at the same stage of their oscillation. The energy transferred by a wave depends on its amplitude (approximately proportional to amplitude squared for mechanical waves), while the frequency is fixed by the source and does not change when the wave enters a new medium.

Edexcel alignment: This content is aligned with Edexcel GCSE Combined Science (1SC0) Physics Topic 4 Waves / Topic 5 Light and the electromagnetic spectrum — specifically CP12 Waves; 4.1 transverse and longitudinal wave properties; 4.2 amplitude, wavelength, frequency and period definitions. Assessed on Physics Paper 2.