Physics 9702 · syllabus 7
Cambridge A Level Physics 9702 — Waves topical past papers
Progressive waves and the energy they carry: v = fλ, intensity, transverse and longitudinal waves, the Doppler effect, the EM spectrum and polarisation.
- Questions
- 517
- Years
- 2009–2026
- With mark scheme
- 100%
- Questions 2022–2026
- 199
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What Waves covers
A progressive wave transfers energy without transferring matter. Each point on it oscillates about its rest position, and displacement, amplitude, period, frequency, wavelength, phase difference and speed describe that motion. From the definitions of speed, frequency and wavelength you derive v = fλ. Intensity is power per unit area and is proportional to the square of the amplitude, and you should be able to read frequency and amplitude from an oscilloscope trace using its time-base and y-gain settings.
In a transverse wave the oscillations are at right angles to the direction of energy transfer; in a longitudinal wave they are along it, forming compressions and rarefactions. Only transverse waves can be polarised, and Malus's law gives the intensity a polarising filter transmits, I = I₀ cos²θ. All electromagnetic waves are transverse and travel at the same speed c in free space; you need the approximate wavelengths of each region, with visible light from about 400 to 700 nm.
When a source of sound moves relative to a stationary observer, the observed frequency rises as it approaches and falls as it moves away: the Doppler effect. Waves are AS content, examined on Papers 1 and 2. They set up superposition in the next topic, and the same frequency-shift idea, applied to light from distant galaxies, returns as redshift in astronomy and cosmology.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- 7 Waves
- 7.1 Progressive waves
- 7.2 Transverse and longitudinal waves
- 7.3 Doppler effect for sound waves
- 7.4 Electromagnetic spectrum
- 7.5 Polarisation
What you should be able to do
- Derive v = fλ from the definitions of speed, frequency and wavelength
- Determine frequency and amplitude from an oscilloscope trace using the time-base and y-gain
- Use intensity = power/area and intensity ∝ amplitude²
- Interpret displacement–distance and displacement–time graphs for transverse and longitudinal waves
- Calculate the frequency heard from a moving source using the Doppler equation
- Apply Malus's law to polarised light passing through one or more polarising filters
Key ideas
- Wave equation v = fλ; period T = 1/f
- Intensity = power/area (W m⁻²), and intensity ∝ (amplitude)²
- Doppler effect for a moving source: fₒ = fₛv/(v ± vₛ), with v − vₛ when the source approaches and v + vₛ when it recedes
- Malus's law I = I₀ cos²θ, θ being the angle between the plane of polarisation and the filter's transmission axis
- Electromagnetic waves travel at c = 3.00 × 10⁸ m s⁻¹ in free space; visible light spans about 400–700 nm
How Waves has been examined
From 2022 to 2026, Waves was on Paper 2 · AS Level Structured Questions in 10 of 11 exam series, worth about 14% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 1 · Multiple Choice | 164 | 13% | 11 of 11 |
| Paper 2 · AS Level Structured Questions | 30 | 14% | 10 of 11 |
| Paper 4 · A Level Structured Questions | 5 | 2% | 3 of 11 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 1.
Filed in Momentum under: Waves.
A worked example
A car horn emits sound of frequency 600 Hz. The car drives at 25 m s⁻¹ past a stationary listener. The speed of sound is 340 m s⁻¹. Find the frequency heard as the car approaches and as it moves away.
- Approaching: fₒ = fₛv/(v − vₛ) = 600 × 340 / (340 − 25)
- = 600 × 340 / 315 = 648 Hz
- Moving away: fₒ = 600 × 340 / (340 + 25) = 600 × 340 / 365 = 559 Hz
- Check: the approaching frequency is above 600 Hz and the receding one below it, as expected
Answer: 648 Hz as it approaches; 559 Hz as it moves away
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Choosing the wrong sign in the Doppler equation — an approaching source must give a higher observed frequency, so the denominator is v − vₛ; check your answer against that
- Using cos θ instead of cos²θ in Malus's law — the amplitude falls by cos θ, but intensity depends on amplitude squared, so it falls by cos²θ
- Reading a wavelength from a displacement–time graph — the repeat interval on a time axis is the period, not the wavelength
- Assuming that doubling the amplitude doubles the intensity — intensity depends on amplitude squared, so it increases four times
- Counting divisions on an oscilloscope screen but forgetting to multiply by the time-base setting, or reading ms/div as s/div
Exam technique
- On oscilloscope questions, measure across several complete cycles and divide, rather than reading a single cycle
- For phase difference, express a path or time difference as a fraction of a wavelength or period and multiply by 360° or 2π rad
- When comparing transverse and longitudinal waves, write about the direction of oscillation relative to the direction of energy transfer, and give an example of each
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.