The Doppler effect, explained with examples

By Ashraf Bhura, Co-Founder, STEM-Tutor · Updated October 2026

When an ambulance races past, its siren drops in pitch. That change is the Doppler effect: the observed frequency of a wave changes when the source or the observer is moving. It explains everything from speed cameras to the expanding universe.

Why it happens

A source emits wavefronts at a steady rate. If the source is still, the wavefronts spread out as evenly spaced circles. If the source moves, each new wavefront is emitted from a point further along its path. Ahead of the source, the wavefronts are squashed closer together, so the wavelength is shorter. Behind the source, they are stretched further apart, so the wavelength is longer.

The wave speed through the air does not change. Since v = fλ, a shorter wavelength means a higher frequency, and a longer wavelength means a lower frequency. For sound, frequency is pitch, so an approaching siren sounds higher and a receding siren sounds lower. The source itself never changes its frequency; only what the observer receives changes.

The formula for sound

For sound with speed v in still air, a source of frequency f, a source moving at v_s and an observer moving at v_o:

f' = f × (v ± v_o) / (v ∓ v_s)

Rather than memorising signs, use the physics: motion towards each other raises the frequency, motion apart lowers it. Choose the sign in the numerator and denominator that makes f' bigger for approaching motion and smaller for separating motion.

• Source approaching a stationary observer: f' = f × v/(v − v_s).
• Source moving away: f' = f × v/(v + v_s).
• Observer approaching a stationary source: f' = f × (v + v_o)/v.
• Observer moving away: f' = f × (v − v_o)/v.

Worked examples

Example 1: an approaching siren

An ambulance siren emits 700 Hz and moves towards you at 30 m/s. The speed of sound is 340 m/s. What frequency do you hear?

• Source approaching: f' = 700 × 340/(340 − 30) = 700 × 340/310.
• f' ≈ 768 Hz, higher than 700 Hz.

Example 2: the same siren moving away

After it passes, what frequency do you hear?

• Source receding: f' = 700 × 340/(340 + 30) = 700 × 340/370.
• f' ≈ 643 Hz. The drop from about 768 Hz to 643 Hz is the familiar “neee-yowww” as it passes.

Example 3: a moving observer

A cyclist rides at 10 m/s towards a stationary speaker playing 500 Hz. What frequency does the cyclist hear? (v = 340 m/s)

• Observer approaching: f' = 500 × (340 + 10)/340.
• f' ≈ 515 Hz.

Example 4: finding the speed of a source

A train horn of 400 Hz is heard at 420 Hz as the train approaches. Find the train's speed. (v = 340 m/s)

• 420 = 400 × 340/(340 − v_s), so 340 − v_s = 400 × 340/420 ≈ 323.8.
• v_s ≈ 16.2 m/s, about 58 km/h.

Sonic booms

As a source's speed approaches the speed of sound, the wavefronts ahead of it bunch closer and closer. At exactly the speed of sound they pile up on top of each other, and above it they form a cone-shaped shock wave behind the source. When that cone sweeps past you, you hear a sudden loud bang: a sonic boom. The formula above stops working at this point, because the denominator v − v_s reaches zero.

The Doppler effect for light

Light waves show the same effect. A light source moving away from us has its wavelengths stretched towards the red end of the spectrum: this is red shift. A source moving towards us shows blue shift. For speeds much less than the speed of light, the fractional change in wavelength is approximately v/c:

Δλ/λ ≈ v/c

Example 5: a receding galaxy

A spectral line normally at 656.3 nm is observed at 669.4 nm in light from a galaxy. Estimate the galaxy's speed away from us. (c = 3.0 × 10⁸ m/s)

• Δλ = 13.1 nm, so Δλ/λ ≈ 0.0200.
• v ≈ 0.0200 × 3.0 × 10⁸ ≈ 6.0 × 10⁶ m/s, moving away.

In the 1920s, astronomers found that light from almost every distant galaxy is red-shifted, and that more distant galaxies have greater red shifts. This shows the universe is expanding, and it is one of the key pieces of evidence for the Big Bang theory, a topic in GCSE separate Physics and A level astrophysics.

Uses of the Doppler effect

• Medical ultrasound: Doppler scans measure the speed of blood flow through arteries and the heart.
• Police speed guns: radar or laser reflected from a moving car returns with a shifted frequency, which gives its speed.
• Weather radar: shifts in reflected microwaves show how fast rain and wind are moving.
• Astronomy: red shift measures how fast stars and galaxies are moving, and tiny periodic shifts reveal planets orbiting other stars.

Common mistakes

• Saying the source changes its frequency; only the observed frequency changes.
• Using the wrong sign: approaching must give a higher frequency.
• Thinking the wave speed changes; for sound in still air, it stays the same.
• Confusing loudness with pitch; the Doppler effect changes pitch.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Is the Doppler effect on the AP Physics exams?

Waves, including sound and the Doppler effect, are part of AP Physics 2 in the current course framework. Check the latest Course and Exam Description on AP Central for the exact scope.

Is it in GCSE or A level Physics?

GCSE separate Physics covers red shift as evidence for the expanding universe. A level Physics covers the Doppler effect for sound and light, especially in the astrophysics option.

Key takeaways

• A moving source squashes waves ahead and stretches them behind.
• Approaching gives a higher frequency; receding gives a lower one.
• For sound: f' = f(v ± v_o)/(v ∓ v_s), signs chosen by the physics.
• For light: Δλ/λ ≈ v/c; receding sources are red-shifted.
• Red shift of distant galaxies shows the universe is expanding.

Related guides

• The electromagnetic spectrum
• A level Physics waves
• AP Physics 2 units