What is the Doppler effect for sound waves in Physics?

The Doppler effect for sound waves is a phenomenon observed when there is a relative motion between a sound source and an observer. It results in a change in the frequency of the sound waves perceived by the observer. If the source is moving towards the observer, the frequency appears higher (a higher pitch), and if moving away, the frequency appears lower (a lower pitch). This concept is an essential part of the Cambridge International A Levels Physics curriculum under the topic of Waves.

How does the Doppler effect apply to sound waves in everyday life?

In everyday life, the Doppler effect for sound waves can be observed when a vehicle with a siren, such as an ambulance or police car, passes by. As the vehicle approaches, the siren's pitch sounds higher, and as it moves away, the pitch drops. This change in pitch is due to the Doppler effect, where the motion of the source relative to the observer alters the frequency of the sound waves reaching the observer.

How can the Doppler effect for sound waves be mathematically expressed?

The Doppler effect for sound waves can be mathematically expressed using the formula: f' = f * (v + vo) / (v + vs), where f' is the observed frequency, f is the emitted frequency, v is the speed of sound in the medium, vo is the velocity of the observer relative to the medium, and vs is the velocity of the source relative to the medium. This formula helps in calculating the perceived frequency when either the source or the observer is in motion.

What factors affect the Doppler effect for sound waves?

The Doppler effect for sound waves is influenced by several factors, including the speed of the sound source, the speed of the observer, and the speed of sound in the medium. Additionally, the direction of motion of both the source and the observer relative to each other also plays a crucial role. These factors collectively determine the change in frequency perceived by the observer.

Why is the Doppler effect important in the study of waves in Physics?

The Doppler effect is important in the study of waves in Physics because it provides insights into how wave frequencies are perceived differently due to motion. It has practical applications in various fields such as astronomy, radar and sonar technology, and medical imaging. Understanding this effect is crucial for Cambridge International A Levels students as it helps in comprehending wave behavior and its implications in real-world scenarios.

Why is "Wrong sign in denominator" a common mistake in Doppler effect for sound waves?

Why it happens: Sign confusion. How to avoid it: Source APPROACHING → use v - v_s (smaller denominator → higher f_o). RECEDING → v + v_s. Source: 9702 Examiner Reports 2022-2024

WavesCambridge International A Levels Physics (9702)

Doppler effect for sound waves

Work through the notes, try the practice questions, then take the quiz. The report tells you exactly what to revise next.

Previous Next

Learn this Topic

Start with the slides for the quick version, then go deeper with the full study notes.

Short Study Notes in the form of Slides

Read the notes first. If the method in a worked example clicks, you're ready for the questions.

Page 1 / 0

Detailed Notes

Full prose, callouts and a recap — built for A* mastery, not just a quick scan.

Take these study notes with you

Download a branded PDF — full prose, callouts, recap and memorise list for Doppler effect for sound waves, ready to print or save offline.

Doppler Effect Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Frequency change due to relative motion. Formulas for source motion. Application to light (redshift).

What you’ll learn

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

7.3.1 — Describe Doppler effect.
7.3.2 — Apply formula for moving source.
7.3.3 — Compute speed from frequency shift.

Doppler effect

Wavefronts compress (approach) or spread (recede).

Effect. When source approaches observer, successive wavefronts arrive more frequently → observed frequency HIGHER. When receding, observed frequency LOWER.

Formula (moving source, stationary observer). $f_o = f_s \frac{v}{v \pm v_s}$

Use $v - v_s$ (denominator smaller) when source APPROACHES.
Use $v + v_s$ when source RECEDES.

Where $v$ = wave speed in medium, $v_s$ = source speed.

Example. Car horn 480 Hz approaching at 25 m/s, $v = 340$ m/s:

$f_o = 480 \times 340/315 \approx 518$ Hz.

Receding: $f_o = 480 \times 340/365 \approx 447$ Hz.

Cambridge tip. Mark scheme awards correct sign + magnitude.

A moving source compresses wavefronts in front (higher observed frequency) and stretches them behind (lower observed frequency).

Approach: $v - v_s$ , higher $f$ .
Recede: $v + v_s$ , lower $f$ .
Sound speed ~340 m/s.

See the full worked example for doppler effect for sound waves →

Doppler for light

Redshift and blueshift.

Non-relativistic formula (for $v \ll c$ ). $\frac{\Delta\lambda}{\lambda} = \frac{\Delta f}{f} = \frac{v}{c}$

Redshift. Observed $\lambda$ longer than emitted → source receding from observer.

Blueshift. Observed $\lambda$ shorter than emitted → source approaching.

Cosmic recession. Distant galaxies show large redshifts → universe expanding (Hubble's law).

Example. Galaxy line at 658 nm; lab line 656 nm.

$\Delta\lambda = 2$ nm.
$v = (\Delta\lambda/\lambda) \cdot c = (2/656)(3 \times 10^8) \approx 9.15 \times 10^5$ m/s.

Cambridge tip. Only use formula when $v \ll c$ .

$\Delta\lambda/\lambda = v/c$ .
Redshift: receding; blueshift: approaching.
Used in astronomy.

See the full worked example for doppler effect for sound waves →

How it’s examined

Doppler typically a single 6-mark question per paper. Most-tested: source-motion formula (5-7 marks), redshift calculation (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.

Master this Topic

Worked examples, formulae, definitions and the mistakes examiners flag — everything you need to push from a pass to an A*.

Take this whole topic with you

Download a branded revision sheet — worked examples, formulae, definitions and common mistakes for Doppler effect for sound waves, ready to print or save as PDF.

Step-by-step worked examples — Doppler effect for sound waves

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

1Source approaching (6 marks)
Extended• Adapted from 9702/22 May/Jun 2024• Doppler
Question
A car horn sounds at 480 Hz. Car approaches at 25 m/s. Speed of sound is 340 m/s. Find observed frequency. (6 marks)
Step-by-step solution
1. Step 1
  Source moving towards stationary observer:
  $f_o = f_s \dfrac{v}{v - v_s}$
2. Step 2
  Substitute.
  $f_o = 480 \times \dfrac{340}{340 - 25} = 480 \times \dfrac{340}{315} \approx 518 \text{ Hz}$
Answer
$f_o \approx 518$ Hz.
2Source receding (5 marks)
Extended• Doppler
Question
Same horn (480 Hz, 25 m/s, $v = 340$ m/s) — car now receding. Find observed frequency. (5 marks)
Step-by-step solution
1. Step 1
  Receding: use $v + v_s$ in denominator.
  $f_o = 480 \times \dfrac{340}{340 + 25} = 480 \times \dfrac{340}{365} \approx 447 \text{ Hz}$
Answer
$f_o \approx 447$ Hz.
3Doppler shift in astronomy (5 marks)
Extended• redshift
Question
Light from a galaxy shows wavelength 658 nm; expected 656 nm. Find the galaxy's recession speed. ( $c = 3 \times 10^8$ m/s.) (5 marks)
Step-by-step solution
1. Step 1
  $\Delta\lambda/\lambda = v/c$ (for $v \ll c$ ).
  $\dfrac{2}{656} = \dfrac{v}{3 \times 10^8}$
2. Step 2
  Solve.
  $v = \dfrac{2}{656} \times 3 \times 10^8 \approx 9.15 \times 10^5 \text{ m/s}$
Answer
$v \approx 9.15 \times 10^5$ m/s (recession).

Key Formulae — Doppler effect for sound waves

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

Doppler — moving source
$f_o = f_s \dfrac{v}{v \pm v_s}$
$f_s$
source frequency
$v$
wave speed (in medium)
$v_s$
source speed
When to use
Use $-$ when source APPROACHES observer; use $+$ when source RECEDES.
Light Doppler (non-relativistic)
$\dfrac{\Delta\lambda}{\lambda} = \dfrac{\Delta f}{f} = \dfrac{v}{c}$
When to use
For light or radio waves at $v \ll c$ . Redshift if receding; blueshift if approaching.

Key Definitions and Keywords — Doppler effect for sound waves

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

Doppler effect
Examiner keyword
Apparent change in frequency due to relative motion between source and observer.
Redshift
Observed wavelength longer than emitted — source receding.
Blueshift
Observed wavelength shorter than emitted — source approaching.

Common Mistakes and Misconceptions — Doppler effect for sound waves

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

✕Wrong sign in denominator
9702 Examiner Reports 2022-2024
Why it happens
Sign confusion.
How to avoid it
Source APPROACHING → use $v - v_s$ (smaller denominator → higher $f_o$ ). RECEDING → $v + v_s$ .

Practice questions

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

Past paper style quiz

Get a report showing which sub-topics you've nailed and which ones still need work.

Video lesson

Short walkthrough of the concepts students most often get stuck on.