What are the basic properties of waves studied in the Cambridge IGCSE Coordinated Science curriculum?

In the Cambridge IGCSE Coordinated Science curriculum, the basic properties of waves include wavelength, frequency, amplitude, speed, and period. These properties help describe how waves, such as light and sound, behave and interact with their environment.

How is wave speed calculated in the context of General Wave Properties?

Wave speed is calculated using the formula: speed = frequency × wavelength. This relationship is crucial in understanding how quickly a wave travels through a medium. For example, in the case of sound waves, this formula helps determine how fast sound travels through air or other materials.

What is the difference between transverse and longitudinal waves in terms of wave properties?

Transverse waves, such as light waves, have oscillations that are perpendicular to the direction of wave travel. Longitudinal waves, like sound waves, have oscillations that are parallel to the direction of wave travel. Understanding these differences is essential in the study of wave properties in the Cambridge IGCSE Coordinated Science curriculum.

Why is understanding wave frequency important in the study of light and sound?

Wave frequency, measured in hertz (Hz), indicates how many wave cycles pass a point per second. In light, frequency determines color, while in sound, it determines pitch. Understanding frequency is crucial for analyzing how different waves interact with materials and affect our perception of light and sound.

How do amplitude and wavelength affect the energy of a wave?

The amplitude of a wave is related to its energy; higher amplitude means more energy. Wavelength, the distance between successive crests or troughs, also affects energy, especially in electromagnetic waves. In the Cambridge IGCSE Coordinated Science curriculum, students learn that shorter wavelengths generally carry more energy, which is why ultraviolet light is more energetic than visible light.

Why is "Confusing amplitude with wavelength or frequency" a common mistake in General Wave Properties?

Why it happens: Students mix up the three quantities described on a wave diagram. How to avoid it: Amplitude = height of wave above equilibrium (vertical). Wavelength = horizontal distance for one full cycle. Frequency = number of complete waves per second.

Why is "Stating that sound is a transverse wave" a common mistake in General Wave Properties?

Why it happens: Sound waves are often drawn on paper as a sine curve, which looks transverse. How to avoid it: Sound is longitudinal — particles vibrate parallel to the direction of travel. The sine curve is a representation of pressure variation, not displacement perpendicular to travel.

Why is "Stating that diffraction is greatest when the gap is much larger than the wavelength" a common mistake in General Wave Properties?

Why it happens: Remembering the relationship backwards. How to avoid it: Maximum diffraction when gap wavelength. Large gap → small diffraction (waves mostly pass straight through).

Properties of Waves, including Light and SoundCambridge IGCSE Coordinated Sciences 0654

General Wave Properties

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General Wave Properties — Cambridge IGCSE Coordinated Science 0654

Waves transfer energy without transferring matter. Cambridge tests transverse vs longitudinal waves, key wave quantities (amplitude, wavelength, frequency, speed), the wave equation v = fλ, and wave behaviours: reflection, refraction, and diffraction.

What you’ll learn

Mapped to the Cambridge IGCSE 0654 syllabus (2025-2027).

P4.1a — Describe transverse and longitudinal waves with examples.
P4.1b — Define amplitude, wavelength, frequency, period, and wave speed.
P4.1c — Recall and use v = fλ and f = 1/T.
P4.1d — Describe and explain reflection, refraction, and diffraction.

Types of Waves and Key Quantities

Know the distinction between transverse and longitudinal, and be able to define all wave quantities.

Transverse waves:

Oscillation is perpendicular (at right angles) to the direction of energy transfer
Can be polarised
Examples: all electromagnetic waves (light, radio, X-rays), water surface waves, waves on a string

Longitudinal waves:

Oscillation is parallel (along) the direction of energy transfer
Consists of compressions (high pressure) and rarefactions (low pressure)
Cannot be polarised
Examples: sound waves, ultrasound, seismic P-waves

Key wave quantities:

Quantity	Symbol	Unit	Definition
Amplitude	A	m	Maximum displacement from equilibrium
Wavelength	λ	m	Distance between two adjacent points in phase (e.g., crest to crest)
Frequency	f	Hz	Number of complete oscillations per second
Period	T	s	Time for one complete oscillation
Wave speed	v	m/s	Speed of wave propagation through the medium

Wave equations:

v = fλ (wave speed = frequency × wavelength) f = 1/T (frequency = 1 / period)

Example: A sound wave has frequency 500 Hz and wavelength 0.66 m. Find its speed.

v = 500 × 0.66 = 330 m/s

Amplitude (A) is the maximum displacement from rest; wavelength (λ) is the distance between successive crests.

Transverse: oscillation ⊥ direction. Longitudinal: oscillation ∥ direction.
v = fλ. f = 1/T.
Amplitude = max displacement. Wavelength = crest-to-crest distance.

Reflection, Refraction, and Diffraction

All waves undergo these three wave behaviours; know the conditions and applications of each.

Reflection:

Wave bounces back at a boundary
Angle of incidence = angle of reflection (measured from normal)
Law of reflection applies to all waves
Applications: mirrors, sonar (echo), radar

Refraction:

Wave changes speed when passing from one medium to another → changes direction (unless hitting boundary at 90°)
If speed decreases → wave bends toward normal
If speed increases → wave bends away from normal
Wavelength changes; frequency stays the same (frequency is fixed by source)
Applications: lenses (light), seismic waves changing speed in different Earth layers

Diffraction:

Waves spread out when passing through a gap or around an obstacle
Effect is most pronounced when: gap width ≈ wavelength
If gap >> wavelength: little diffraction (wave passes straight through)
If gap << wavelength: most energy reflected back
Applications: radio waves diffract around hills; sound diffracts around doors

Comparison:

Behaviour	What changes	What stays the same
Reflection	Direction	Speed, wavelength, frequency
Refraction	Speed, wavelength, direction	Frequency
Diffraction	Direction (spreads)	Speed, wavelength, frequency

Reflection: angle in = angle out (from normal).
Refraction: speed changes → direction changes (f unchanged, λ changes).
Diffraction: maximum when gap ≈ wavelength.

How it’s examined

Paper 4: 'A wave has frequency 250 Hz and wavelength 1.32 m. Calculate the wave speed' (2 marks — v = 250 × 1.32 = 330 m/s). 'Describe the difference between transverse and longitudinal waves' (2 marks — transverse: oscillation perpendicular to direction of travel; longitudinal: oscillation parallel). 'Explain why radio waves diffract more around hills than light waves' (2 marks — radio wavelength much larger; closer to/larger than gap/obstacle size → more diffraction). Draw a wave diagram labelling amplitude and wavelength.

Sources: Cambridge IGCSE Coordinated Sciences 0654 syllabus 2025-2027 (P4); 0654 Examiner Reports 2022-2024. Last reviewed 2026-05-14.

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Step-by-step worked examples — General Wave Properties

Step-by-step solutions to past-paper-style questions on general wave properties, written exactly the way a tutor would explain them at the board.

1Using the wave equation
Core• wave equation, v=fλ
Question
A sound wave in air has a frequency of $440\,\text{Hz}$ and a wavelength of $0.75\,\text{m}$ . Calculate the speed of the wave.
Step-by-step solution
1. Step 1
  Apply the wave equation $v = f\lambda$ .
  $v = 440 \times 0.75 = 330\,\text{m/s}$
Answer
$v = 330\,\text{m/s}$
2Explaining diffraction
Extended• diffraction, gap width, wavelength
Question
Explain what happens when water waves pass through a gap in a barrier, and state the conditions for maximum diffraction.
Step-by-step solution
1. Step 1
  When waves pass through a gap, they spread out (diffract) into the region beyond the gap. The wave pattern beyond the gap is curved, not straight.
2. Step 2
  Diffraction is greatest when the gap width is approximately equal to the wavelength of the wave.
  $\text{Maximum diffraction when} \; d \approx \lambda$
3. Step 3
  If the gap is much larger than the wavelength ( $d \gg \lambda$ ), very little diffraction occurs and the waves mostly pass straight through.
Answer
Waves spread on passing through a gap. Maximum diffraction when gap width $\approx$ wavelength.
3Transverse vs longitudinal — comparing compressions and rarefactions
Challenge• transverse, longitudinal, compression, rarefaction
Question
Compare transverse and longitudinal waves, giving one example of each. For a longitudinal wave, explain what is meant by compression and rarefaction.
Step-by-step solution
1. Step 1
  Transverse wave: particles vibrate perpendicular to the direction of energy transfer. Example: light (electromagnetic waves), water surface waves.
2. Step 2
  Longitudinal wave: particles vibrate parallel to the direction of energy transfer. Example: sound in air.
3. Step 3
  Compression: a region where particles are closer together than normal — higher pressure. Rarefaction: a region where particles are further apart than normal — lower pressure.
Answer
Transverse: vibration perpendicular to propagation (e.g. light). Longitudinal: vibration parallel to propagation (e.g. sound), with alternating compressions (high pressure) and rarefactions (low pressure).

Key Formulae — General Wave Properties

The formulae you need to memorise for general wave properties on the Cambridge IGCSE 0654 paper, with every variable defined in plain English and a note on when to use it.

Wave equation
$v = f\lambda$
$v$
wave speed (m/s)
$f$
frequency (Hz)
$\lambda$
wavelength (m)
When to use
Finding wave speed, frequency, or wavelength from the other two.
Example
$v = 440\,\text{Hz} \times 0.75\,\text{m} = 330\,\text{m/s}$
Period and frequency
$T = \dfrac{1}{f}$
$T$
period (s) — time for one complete oscillation
$f$
frequency (Hz)
When to use
Converting between period and frequency.

Key Definitions and Keywords — General Wave Properties

Definitions to memorise and the exact keywords mark schemes credit for general wave properties answers — sharpened from recent examiner reports for the 2026 0654 sitting.

Amplitude
Examiner keyword
The maximum displacement of a particle from its equilibrium (rest) position. Related to the energy of the wave — greater amplitude means more energy.
Wavelength
Examiner keyword
The distance between two successive points that are in phase (e.g., crest to crest, or compression to compression). SI unit: metre (m).
Frequency
Examiner keyword
The number of complete oscillations (waves) passing a point per second. SI unit: hertz (Hz), where $1\,\text{Hz} = 1\,\text{s}^{-1}$ .
Wavefront
A line or surface connecting all points that are in the same phase of vibration (e.g., all the crests at one instant). Perpendicular to the direction of energy transfer.
Diffraction
Examiner keyword
The spreading of waves as they pass through a gap or around an obstacle. Most pronounced when the gap width is approximately equal to the wavelength.

Common Mistakes and Misconceptions — General Wave Properties

The traps other students keep falling into on general wave properties questions — taken from recent Cambridge IGCSE 0654 examiner reports and mark schemes — and how to avoid them.

✕Confusing amplitude with wavelength or frequency
Why it happens
Students mix up the three quantities described on a wave diagram.
How to avoid it
Amplitude = height of wave above equilibrium (vertical). Wavelength = horizontal distance for one full cycle. Frequency = number of complete waves per second.
✕Stating that sound is a transverse wave
Why it happens
Sound waves are often drawn on paper as a sine curve, which looks transverse.
How to avoid it
Sound is longitudinal — particles vibrate parallel to the direction of travel. The sine curve is a representation of pressure variation, not displacement perpendicular to travel.
✕Stating that diffraction is greatest when the gap is much larger than the wavelength
Why it happens
Remembering the relationship backwards.
How to avoid it
Maximum diffraction when gap $\approx$ wavelength. Large gap → small diffraction (waves mostly pass straight through).

Practice questions

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General Wave Properties — frequently asked questions

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General Wave Properties

Short Study Notes in the form of Slides

Short Study Notes — General Wave Properties

Detailed Notes

What you’ll learn

How it’s examined

1Using the wave equation

2Explaining diffraction

3Transverse vs longitudinal — comparing compressions and rarefactions

Wave equation

Period and frequency

Amplitude

Wavelength

Frequency

Wavefront

Diffraction

✕Confusing amplitude with wavelength or frequency

✕Stating that sound is a transverse wave

✕Stating that diffraction is greatest when the gap is much larger than the wavelength

Practice questions

Past paper style quiz

Assess your understanding

General Wave Properties — frequently asked questions