What are progressive waves in the context of Cambridge International A Levels Physics?

Progressive waves are waves that transfer energy from one point to another without the transfer of matter. In the Cambridge International A Levels Physics curriculum, these waves are studied as they propagate through a medium, characterized by their ability to move energy and information across distances.

How do progressive waves differ from stationary waves?

Progressive waves differ from stationary waves in that they move through a medium, transferring energy from one location to another. In contrast, stationary waves, also known as standing waves, do not transfer energy along the medium; instead, they form a pattern of nodes and antinodes due to the interference of two waves traveling in opposite directions.

What are the key characteristics of progressive waves?

The key characteristics of progressive waves include amplitude, wavelength, frequency, and speed. Amplitude refers to the maximum displacement of points on the wave, wavelength is the distance between successive crests or troughs, frequency is the number of waves passing a point per second, and speed is how fast the wave propagates through the medium.

How is the speed of a progressive wave calculated?

The speed of a progressive wave is calculated using the formula v = fλ, where 'v' represents the wave speed, 'f' is the frequency, and 'λ' (lambda) is the wavelength. This relationship is fundamental in understanding wave behavior in the Cambridge International A Levels Physics syllabus.

What are some real-world examples of progressive waves?

Real-world examples of progressive waves include sound waves traveling through air, water waves moving across the surface of a body of water, and electromagnetic waves such as light traveling through space. These examples illustrate how progressive waves are integral to various physical phenomena studied in Physics.

Why is "Treating intensity proportional to amplitude (not squared)" a common mistake in Progressive waves?

Why it happens: Linear relationship habit. How to avoid it: I A^2. Doubling amplitude × 4 the intensity. Source: 9702 Examiner Reports 2022-2024

WavesCambridge International A Levels Physics (9702)

Progressive waves

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Progressive Waves Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Wave properties and the wave equation $v = f\lambda$ . Phase. Intensity.

What you’ll learn

Mapped to the Cambridge IGCSE 9702 syllabus (2025-2027).

7.1.1 — Describe wave properties.
7.1.2 — Use $v = f\lambda$ .
7.1.3 — Understand phase difference.

Wave properties

Wavelength, frequency, period, amplitude.

Progressive wave. Transfers energy without net transfer of matter.

Key quantities.

Wavelength $\lambda$ : distance between adjacent points in phase. Units m.
Frequency $f$ : oscillations per second. Units Hz.
Period $T$ : time for one oscillation. $T = 1/f$ . Units s.
Amplitude $A_0$ : max displacement from equilibrium.
Speed $v$ : distance wavefront travels per second.

Wave equation. $v = f\lambda$ . Universal — works for any wave.

Phase. Position in oscillation cycle. Two points 'in phase' have phase difference $0$ or $2\pi$ . 'Antiphase' = $\pi$ .

Cambridge tip. All five symbols must be defined.

Wavelength, frequency, period, amplitude.
$v = f\lambda$ universal.
$T = 1/f$ .

See the full worked example for progressive waves →

Intensity

Power per unit area.

Intensity. $I = P/A$ where $P$ is power and $A$ is area perpendicular to propagation.

Units. W/m².

Key relation. $I \propto A_0^2$ (amplitude SQUARED).

Inverse square law. Point source emitting uniformly in all directions: $I = \frac{P}{4\pi r^2}$ Intensity falls as $1/r^2$ .

Example. Doubling amplitude → intensity × 4.

Cambridge tip. $I \propto A_0^2$ is examiner favourite.

$I = P/A$ .
$I \propto A_0^2$ .
Inverse square law for point source.

See the full worked example for progressive waves →

Phase

Position in cycle.

Phase difference between two oscillating quantities measured in radians (or degrees).

Common phase differences.

$0$ or $2\pi$ : in phase.
$\pi/2$ : quarter cycle (90°).
$\pi$ : antiphase (180°).

Phase between two points on a progressive wave separated by distance $d$ : $\Delta\phi = \frac{2\pi d}{\lambda}$

Example. Two points $\lambda/4$ apart: phase difference $\pi/2$ .

Cambridge tip. State units (radians/degrees) explicitly.

Phase in radians or degrees.
$\Delta\phi = 2\pi d/\lambda$ .
Same value = in phase.

How it’s examined

Progressive waves on every Paper 1. Most-tested: $v = f\lambda$ (4-5 marks), intensity-amplitude (5 marks), phase (5 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/22 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

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Step-by-step worked examples — Progressive waves

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

1Wave equation (4 marks)
Extended• Adapted from 9702/22 May/Jun 2024• wave equation
Question
A water wave has wavelength 0.50 m and frequency 4.0 Hz. Find its speed. (4 marks)
Step-by-step solution
1. Step 1
  $v = f\lambda$ .
  $v = 4.0 \times 0.50 = 2.0 \text{ m/s}$
Answer
$v = 2.0$ m/s.
2Period and frequency (4 marks)
Extended• period
Question
A wave has period 0.020 s. Find frequency. (4 marks)
Step-by-step solution
1. Step 1
  $f = 1/T$ .
  $f = 1/0.020 = 50 \text{ Hz}$
Answer
$f = 50$ Hz.
3Intensity vs amplitude (5 marks)
Extended• intensity
Question
Wave amplitude is doubled. By what factor does intensity change? (5 marks)
Step-by-step solution
1. Step 1
  Intensity $\propto A^2$ .
2. Step 2
  Amplitude doubled → intensity multiplied by $2^2 = 4$ .
Answer
Intensity quadruples (×4).

Key Formulae — Progressive waves

The formulae you need to memorise for progressive waves on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Wave equation
$v = f\lambda$
$v$
wave speed
$f$
frequency
$\lambda$
wavelength
When to use
All waves. Universal.
Frequency-period
$f = \dfrac{1}{T}$
$T$
period
When to use
Period and frequency are reciprocals.
Intensity
$I = \dfrac{P}{A} \propto A_0^2$
$P$
power
$A$
area
$A_0$
amplitude
When to use
Wave power per unit area. Proportional to amplitude squared.

Key Definitions and Keywords — Progressive waves

Definitions to memorise and the exact keywords mark schemes credit for progressive waves answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Progressive wave
Examiner keyword
A wave that transfers energy without net transfer of matter.
Wavelength
Examiner keyword
Distance between two adjacent points oscillating in phase. Symbol $\lambda$ , units m.
Frequency
Examiner keyword
Number of complete oscillations per second. Symbol $f$ , units Hz.
Period
Examiner keyword
Time for one complete oscillation. $T = 1/f$ . Units s.
Amplitude
Examiner keyword
Maximum displacement from equilibrium position.
Phase difference
Fraction of a cycle between two points or two waves. Measured in radians or degrees.

Common Mistakes and Misconceptions — Progressive waves

The traps other students keep falling into on progressive waves questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Treating intensity proportional to amplitude (not squared)
9702 Examiner Reports 2022-2024
Why it happens
Linear relationship habit.
How to avoid it
$I \propto A^2$ . Doubling amplitude × 4 the intensity.

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

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Video lesson

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Progressive waves — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Progressive waves

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1Wave equation (4 marks)

2Period and frequency (4 marks)

3Intensity vs amplitude (5 marks)

Wave equation

Frequency-period

Intensity

Progressive wave

Wavelength

Frequency

Period

Amplitude

Phase difference

✕Treating intensity proportional to amplitude (not squared)

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Progressive waves — frequently asked questions