SoundExtendabout 45 min

Doppler shifts, digital recording and listening to the Earth

The physics of a passing siren, why your recorded voice sounds strange, and how earthquakes get located

Work out how much a siren's pitch shifts as it passes, find out why your recorded voice sounds strange (a real anatomical reason), and see why 44,100 Hz was not an arbitrary choice. Try two projects, solve combined puzzles, and use sound's own reasoning to locate an earthquake.

Start at chapter 1

In this part you’ll

Calculate the Doppler-shifted frequency of an approaching or receding source, and explain why a source's own listener hears no shift.
Explain redshift and blueshift as light's Doppler effect, and name one everyday and one astronomical use.
Explain digital sampling and why 44,100 Hz was chosen, and trace the round trip from voice to file and back.
Explain bone conduction and why a recorded voice differs from how a speaker hears themselves.
Use P and S wave speeds to find the distance to an earthquake, and explain why three stations are needed to locate it.

Four layers in, you can explain almost any everyday sound question with real numbers. Extend takes you past the school syllabus into the physics of a passing siren, the engineering choice behind every music file you own, a strange fact about your own voice, two real research careers, and a handful of puzzles designed to make you combine everything you know at once.

Chapter 01

The Doppler effect, precisely

A motorbike approaches, honking steadily, and passes you. The note is not constant: it sounds higher as it approaches and drops to something noticeably lower the instant it passes, even though the rider's hand never touches the horn button differently. This is the Doppler effect, named after the Austrian physicist Christian Doppler, who proposed it in 1842.

f' = f × v ÷ (v − vₛ)

Frequency heard as the source approaches. f is the source's true frequency, v is the speed of sound, vₛ is the source's speed.

f' = f × v ÷ (v + vₛ)

Frequency heard as the source recedes: the sign in the bracket flips.

Worked example

0 / 5 steps shown

A scooter horn, approaching and receding

A scooter's horn sounds at 300 Hz. The scooter moves at 30 km/h. What frequency do you hear as it approaches, and as it drives away? (Speed of sound = 343 m/s.)

Need a different angle?

TableHow much the Doppler effect shifts a few real, moderate speeds (speed of sound = 343 m/s)
Source	True note	Speed	Heard approaching	Heard receding
Scooter horn	300 Hz	30 km/h	307.5 Hz	292.9 Hz
Car horn	400 Hz	72 km/h	424.8 Hz	377.5 Hz
Train horn	350 Hz	80 km/h	374.2 Hz	328.7 Hz
Ambulance siren	700 Hz	120 km/h	775.3 Hz	638.0 Hz

Predict first

A rider sitting on the motorbike, right next to its own horn, listens as the bike accelerates from a stop up to 80 km/h. What frequency change does the rider hear from their own horn?

The same rise and fall a bystander would hearNone: the horn's frequency relative to the rider never changesOnly a rise, never a fallA much bigger shift than a bystander hears

Try it

Lab

Connect eight terms from this layer to their meanings.

Match each term from this layer to its meaning.

8 pairs are hiding in two mixed-up columns. Pick one from each side to join them.

Text version of this activity

A matching game with eight pairs covering this layer's core vocabulary: the Doppler effect, redshift, sampling rate, the Nyquist-Shannon theorem, bone conduction, P waves, S waves and triangulation, each matched to a plain-English meaning.

Example

What happens if a source reaches the speed of sound itself

The approaching Doppler formula divides by (v − vₛ). As a source's speed vₛ gets closer and closer to the speed of sound v, that bottom number shrinks towards zero, and the formula predicts an ever more extreme, and finally undefined, frequency.

Real supersonic aircraft do not defy this; they simply leave the ordinary wave picture behind. Instead of spreading outward smoothly ahead of the plane, the compressions pile up into a single, very strong pressure wave trailing behind it in a cone shape: the sonic boom, heard on the ground as one sharp crack rather than a smoothly rising note. It is a genuinely different regime of physics from anything else in this topic, mentioned here only so the formula's own breaking point makes sense.

Lab

Sort six situations into pitch rises, pitch falls, or no change, using the Doppler effect.

Sort each situation by whether the heard pitch rises, falls, or stays the same.

6 cards, 3 bins. Tap a card, then tap its bin. You can also drag, or press a bin’s number key.

Text version of this activity

A sorting game with six cards and three bins: pitch rises, pitch falls and no change.

Rises: an ambulance approaching, and a thrown cricket ball approaching a wicketkeeper. Falls: the same ambulance after it passes, and a train horn the instant it passes you. No change: a rider listening to their own horn (no relative motion), and a parked car's horn heard by a passing walker (the source itself is not moving).

The test behind every card: is the source moving relative to the listener, and if so, in which direction?

Chapter 02

Doppler beyond sound

Christian Doppler's original 1842 proposal was actually about light and colour, not sound; sound was confirmed to show the same effect within a few years, and it is sound where most people first meet the idea. But the underlying reasoning, waves bunching up ahead of an approaching source and stretching out behind a receding one, applies to any wave at all, including light.

Related to

Light

Redshift and blueshift are light's own Doppler effect: the same reasoning about waves bunching up or stretching out, applied to light instead of sound.

Worked example

0 / 6 steps shown

How a police radar gun measures speed from a Doppler shift

An X-band radar gun sends out a 10.525 GHz radio wave. It reflects off an approaching car and returns with its frequency shifted by 2,106.5 Hz. Given that the shift is Δf = 2 × f₀ × v ÷ c (the factor of 2 because the wave makes a there-and-back trip), find the car's speed.

Need a different angle?

Worked example

0 / 5 steps shown

Estimating a galaxy's recession speed from redshift

A particular spectral line normally at a wavelength of 500 nanometres is measured, from a distant galaxy's light, at 500.5 nanometres: a shift of 0.5 nm towards red. Using the slow-speed approximation v ≈ c × Δλ ÷ λ, estimate the galaxy's recession speed.

Need a different angle?

Chapter 03

How sound becomes a file

A microphone, from the Investigate layer, turns sound into a smoothly, continuously changing electric current. A digital recording cannot store something smooth and continuous; a computer only stores numbers. So somewhere between the microphone and the file on your phone, that smooth signal has to be chopped into a very long list of numbers, a process called sampling.

Worked example

0 / 5 steps shown

Why 44,100, and not some smaller, tidier number?

Human hearing reaches about 20,000 Hz. The Nyquist-Shannon sampling theorem says you must sample at more than twice the highest frequency you want to capture. What is the minimum sampling rate this theorem allows for full-range human hearing, and how does the CD standard of 44,100 Hz compare?

Need a different angle?

TableSampling rates in everyday and specialist use
Use	Sampling rate	Highest frequency captured
Old analogue telephone calls	8,000 Hz	4,000 Hz: enough for speech to be understood, not for music
CD-quality audio	44,100 Hz	22,050 Hz: comfortably above the top of human hearing
Professional studio recording	96,000 or 192,000 Hz	48,000 or 96,000 Hz: far more headroom than hearing needs
Recording a bat's ultrasonic calls	250,000 Hz or higher	125,000 Hz or higher: needed to capture calls up to about 120,000 Hz

Worked example

0 / 4 steps shown

Why bat-recording equipment needs such a high sampling rate

A bat researcher wants to record calls up to 120,000 Hz without losing information. Using the Nyquist-Shannon rule (sample at more than twice the highest frequency), what minimum sampling rate is needed, and why would an ordinary 44,100 Hz voice recorder be useless for this?

Need a different angle?

Step through

From your voice to a saved file, and back again

Step 1 of 6

You speak

Your vocal folds vibrate, and the resulting sound wave, compressions and rarefactions in air, reaches a microphone.

All steps

: Your vocal folds vibrate, and the resulting sound wave, compressions and rarefactions in air, reaches a microphone.
: The microphone's diaphragm and coil turn the arriving sound into a smoothly, continuously changing electric current, exactly matching the sound wave's shape.
: An analogue-to-digital converter measures the current's exact height 44,100 times every second (for CD-quality audio) and stores each measurement as a number.
: Millions of these numbers, one after another, are saved to a file, sometimes compressed to take up less storage space.
: A digital-to-analogue converter reads the saved numbers back out, 44,100 a second, and recreates a smoothly changing electric current from them.
: The rebuilt current drives a loudspeaker's coil and cone, recreating compressions and rarefactions in the air: your recorded voice, played back.

Text version of this activity

A six-step round trip. Your voice makes a sound wave, a microphone turns it into a matching electric current, an analogue-to-digital converter samples that current 44,100 times a second and stores the results as numbers, the numbers are saved to a file, a digital-to-analogue converter rebuilds a current from them on playback, and a loudspeaker turns that current back into sound. Every digital recording you have ever heard, on a phone, in a film or on a streaming service, follows this same six-step round trip.

Chapter 04

Why your recorded voice sounds strange

Almost everyone's first reaction to hearing their own recorded voice is the same: "that doesn't sound like me." It is a completely genuine difference, not just unfamiliarity, and the reason is a second path sound takes that has nothing to do with air at all.

Aha

You hear two versions of your own voice; nobody else does

When you talk, sound reaches your own ears by two routes at once: through the air, exactly as it reaches anyone listening to you, and through the bones of your skull, bypassing the outer ear entirely.

Bone conducts low frequencies particularly well, so the bone-conduction path adds extra bass, richness and depth to the voice you hear inside your own head. Everyone else only ever gets the air-conducted version.

A microphone, like everyone else's ears, only picks up the air-conducted sound. So a recording plays back exactly what other people already hear you as, missing only the private, bone-added richness you are used to hearing from the inside. The recording is not wrong; your own everyday impression of your voice was always the unusual one.

Related to

Anatomy of the human body

Bone conduction depends on the skull's bones carrying vibration directly to the inner ear, a different route through the body's anatomy from the usual air-and-eardrum path.

Chapter 05

Project: measure a Doppler shift yourself

Recording and measuring a real Doppler shift

Step 01Find a safe, steady sound sourcesafety first
Stand well back from any road. A passing train with a horn, a car with hazard-light clicking loud enough to hear, or (with an adult's help) a phone playing a steady tone from a bicycle rolling past are all safer than standing near traffic.
Step 02Record it approaching and recedingphone microphone
Record continuously as the source approaches, passes, and moves away, ideally standing to one side rather than directly in its path.
Step 03Look at the recording as a spectrogramfree software
Free audio-editing software (many are available for computers and some for phones) can display a spectrogram: a graph of frequency against time. The pitch trace should visibly step down as the source passes.
Step 04Estimate the frequency before and afterread the graph
Read off the approximate frequency just before and just after the moment of passing directly opposite you, which is where the shift is sharpest.
Step 05Compare with the formulacheck your physics
If you can estimate the source's speed (a train timetable, a car's approximate speed, a measured cycling speed), use f' = f × v ÷ (v ∓ vₛ) with the frequency before passing to predict the frequency after, and compare with what you measured.

Reflect

If you tried the Doppler recording project, describe what you measured and how closely it matched the formula's prediction. If you could not try it, describe exactly what equipment and conditions you would need, and predict one source of error that might make a real measurement differ from the formula's clean prediction.

This stays on this page only. It isn’t saved or sent anywhere.

Chapter 06

Project: build a resonance instrument

Understand introduced the jal tarang, tuned bowls of water struck with a stick. Building and tuning your own version by ear, rather than just reading about one, is one of the best ways to feel resonance and mass-loading directly in your hands.

Building and tuning your own eight-note water xylophone

Step 01Gather eight identical bowls or tumblerssame size
Identical containers matter: differences in glass thickness or shape change the note independently of the water level, making tuning confusing.
Step 02Set the two end bowls firstempty and full
The nearly empty bowl will ring highest; the nearly full one will ring lowest, giving you the top and bottom of your scale.
Step 03Tap each bowl and listen for a rough scaletune by ear
Adjust the water in the six middle bowls, a small amount at a time, until each note sounds a clear step higher than the one before it, working from the fullest bowl to the emptiest.
Step 04Check your scale against a known instrumentcompare
Compare against a harmonium, keyboard app or singing voice you trust, adjusting water levels until the steps sound evenly spaced.
Step 05Play a simple, familiar tunetest it
A children's rhyme or a simple film tune is enough to prove the instrument actually works as a scale, not just eight separate notes.

Chapter 07

Puzzles: combine what you know

Worked example

0 / 4 steps shown

The old railway trick

A worker presses an ear to a steel rail 1,000 metres up the line while a hammer strikes the far end once. They also hear the same strike through the air. How much earlier does the sound arrive through the rail than through the air? (Speed in steel = 5,960 m/s; speed in air = 343 m/s.)

Need a different angle?

Worked example

0 / 4 steps shown

A car horn: Doppler and echo together

A car horn sounding at 400 Hz approaches you at 72 km/h (20 m/s). At the same moment, someone claps once beside a wall 686 metres away. (a) What frequency do you hear from the approaching horn? (b) How long does the clap's echo take to return? Treat the two events separately.

Need a different angle?

Worked example

0 / 5 steps shown

Stepping back from a firecracker is not enough on its own

A firecracker measures 140 dB at 2 metres. A bystander moves back to 16 metres away, eight times further. Using level(d₂) = level(d₁) − 20 × log₁₀(d₂ ÷ d₁), how loud does it still seem, and is that safe?

Need a different angle?

Try it

Chapter 08

Wider context: listening to the Earth itself

The thunder rule from Discover, count the seconds and divide, turns out to be one example of a much bigger idea: whenever two signals of different, known speeds set off from the same event at the same instant, the time gap between their arrivals tells you how far away that event happened. Earthquakes give the clearest large-scale example on the whole planet.

Worked example

0 / 4 steps shown

How far away was that earthquake?

A seismograph station records the P wave, then the S wave 20 seconds later. Using approximate crust speeds of 6 km/s (P) and 3.5 km/s (S), how far away was the earthquake?

Need a different angle?

Chapter 09

Careers built on sound

TableA few careers where understanding sound is central
Career	What they do	Sound ideas they use daily
Acoustic (architectural) engineer	Design concert halls, cinemas, offices and classrooms for the right amount of reverberation	Sabine's formula, absorption, reflection
Audiologist	Test hearing, fit hearing aids, diagnose hearing loss	Decibels, frequency range, how the ear works
Sound engineer / Foley artist	Record, mix and create sound for films, music and games	Microphones, digital sampling, timbre and harmonics
Seismologist	Study earthquakes and the Earth's interior using vibration data	P and S waves, wave speed, triangulation
Marine bioacoustician	Study how whales, dolphins and fish use sound underwater	Speed of sound in water, echolocation, infrasound
Ultrasound (sonography) technician	Operate medical ultrasound scanners safely and accurately	Frequency-versus-detail trade-off, echo timing

Reflect

Pick one career from the table above. Write three sentences: what a typical working day might involve, one piece of sound physics from this topic they would use constantly, and one question you would want to ask someone who actually does that job.

This stays on this page only. It isn’t saved or sent anywhere.

Chapter 10

Open questions

Think about it

Nobody has fully solved these yet. Pick one and dig in.

Could a phone app measure a passing vehicle's speed accurately just from the Doppler shift in its recorded horn, without any other sensor? What would make this hard in a noisy street?
Musical pillars exist in several South Indian temples. Could similar acoustic engineering be deliberately designed into a modern building today, and would anyone want it?
As lossy digital compression (used to make music files smaller) keeps improving, is there a point at which nobody could ever hear the difference from an uncompressed recording? How would you test that fairly?
Whales' infrasound calls can apparently travel across whole ocean basins. How does noise from ships affect how far those calls actually carry today?
If a hearing aid could shift ultrasound or infrasound down into the range a person can hear, what new things might they notice about their everyday surroundings?

Reflect

Pick one open question above, or a sound-related open question of your own. Write down one small experiment or piece of research, doable by a school student, that would move it forward even slightly.

This stays on this page only. It isn’t saved or sent anywhere.

Chapter 11

Check what you know

Words to know

All maths vocabulary →

Extend words to keep

Doppler effect: The change in frequency an observer hears because of relative motion between a source and the observer.; Example: A siren sounding higher as it approaches, lower as it recedes.
Redshift / blueshift: Light's Doppler effect: shifted towards red when a source recedes, towards blue when it approaches.; Example: Evidence that most distant galaxies are moving away from Earth.
Sampling: Measuring an audio signal's height at many evenly spaced instants and storing each as a number.; Example: CD audio samples 44,100 times a second.
Sampling rate: How many samples are taken every second, in hertz.; Example: 44,100 Hz for CD-quality audio.
Nyquist-Shannon theorem: The rule that a sampling rate must exceed twice the highest frequency to be captured faithfully.; Example: 40,000 Hz minimum for 20,000 Hz hearing.
Bone conduction: Sound reaching the inner ear through the skull's bones rather than through the air and ear canal.; Example: Why your recorded voice sounds different from how you hear yourself.
P wave: A fast, longitudinal earthquake wave, like sound, travelling through the solid Earth.; Example: About 6 km/s in the upper crust.
S wave: A slower, transverse earthquake wave, more like a shaken rope.; Example: About 3.5 km/s in the upper crust.
Triangulation: Locating an event by combining distance circles from at least three separate measuring stations.; Example: How seismologists pinpoint an earthquake's epicentre.
Sonic boom: The single strong crack heard when a source moves faster than sound, breaking the ordinary Doppler picture.; Example: The sound of a supersonic aircraft passing overhead.
Compression (digital audio): Storing an almost-identical-sounding file in far less space, usually by discarding sound details hearing barely notices.; Example: Why two files at the same sampling rate can differ greatly in size.

Keep this

Cheat sheet

Doppler effect: f' = f × v ÷ (v − vₛ) approaching, f' = f × v ÷ (v + vₛ) receding. No relative motion, no shift, whatever the source's own speed.
Faster sources shift more: vₛ is a bigger share of v (343 m/s), changing the fraction more.
Light shows the same directional idea: redshift for a receding source, blueshift for an approaching one, used in astronomy and radar/speed guns, though the precise maths differs from sound's.
Digital audio samples a signal, typically 44,100 times a second, chosen to exceed twice the 20,000 Hz top of human hearing (the Nyquist-Shannon theorem).
Bone conduction adds extra bass to the voice you hear from inside your own head; a recording captures only what everyone else already hears.
A long steel rail carries sound to a listener's ear far sooner than air does, over 17 times faster, a real, testable effect.
P and S waves from an earthquake travel at different speeds (about 6 and 3.5 km/s); their arrival-time gap gives distance, and three stations' distances triangulate the exact location.
Careers built on sound include acoustic engineering, audiology, sound engineering, seismology, marine bioacoustics and medical sonography.

Where this comes from

Sources

Doppler effect (opens another website) — Encyclopaedia Britannicaawaiting check
Supports the Doppler effect for a passing train horn or ambulance siren, the formulas for an approaching and a receding source, and Christian Doppler's 1842 proposal.
Speed of Sound in Air and Other Materials (opens another website) — HyperPhysics, Georgia State Universityawaiting check
Supports the value 343 m/s in dry air at 20 degrees C, the approximation v = 331.3 + 0.606 x temperature in Celsius, speeds in fresh water, wood and steel, and why stiffness rather than density decides the speed.
44,100 Hz (opens another website) — Wikipediaawaiting check
Supports why digital audio and compact discs sample at 44,100 times a second: the Nyquist-Shannon theorem requires more than twice the highest frequency to be captured, and human hearing reaches about 20,000 Hz.
Bone conduction (opens another website) — Wikipediaawaiting check
Supports why a recorded voice sounds different from how a speaker hears their own voice: bone conduction of the skull adds richer low frequencies that a microphone, using only air conduction, does not pick up.
How do seismologists locate an earthquake? (opens another website) — U.S. Geological Surveyawaiting check
Supports using the time gap between the faster P wave and the slower S wave, recorded at seismograph stations, to work out how far away an earthquake occurred, the same reasoning as the thunder rule.
Sound (Science, Class 9, Chapter 12) (opens another website) — NCERTawaiting check
Supports sound as a vibration needing a medium, the bell-in-a-vacuum-jar experiment, compressions and rarefactions, longitudinal waves, v = f x wavelength, speeds in air, water and steel, echo timing t = 2d/v, reverberation, SONAR, the ear, and the 20 Hz to 20 kHz range.
Sound Waves and Music (opens another website) — The Physics Classroomawaiting check
Supports longitudinal versus transverse waves on a slinky and a rope, pitch and frequency, amplitude and loudness, resonance and standing waves on strings and in air columns, and the mathematics of echo and reverberation.
Frequency of a Police Radar Gun (opens another website) — The Physics Factbook (hypertextbook.com)awaiting check
Supports the operating frequencies of police speed radar: X band at about 10.525 GHz and K band at about 24.15 GHz, used in a worked Doppler-radar example.

End of Extend

What you just read

Calculate the Doppler-shifted frequency of an approaching or receding source, and explain why a source's own listener hears no shift.
Explain redshift and blueshift as light's Doppler effect, and name one everyday and one astronomical use.
Explain digital sampling and why 44,100 Hz was chosen, and trace the round trip from voice to file and back.
Explain bone conduction and why a recorded voice differs from how a speaker hears themselves.
Use P and S wave speeds to find the distance to an earthquake, and explain why three stations are needed to locate it.

The web

Explore a connection

Contrasts with
Light
Both travel as waves and carry energy, but light needs no material and races a million times faster than sound.
Used inanother area
Anatomy of the human body
The ear turns shaking air into signals a nerve can carry: a drum, three tiny bones and a spiral of fluid.
Related to
Electricity
Microphones and speakers turn sound into current and current back into sound.

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Revision 1 · release preview-7e1cbbcc4f · accepted 20/09/2026

A scooter horn, approaching and receding

How a police radar gun measures speed from a Doppler shift

Estimating a galaxy's recession speed from redshift

Why 44,100, and not some smaller, tidier number?

Why bat-recording equipment needs such a high sampling rate

Recording and measuring a real Doppler shift

Building and tuning your own eight-note water xylophone

The old railway trick

A car horn: Doppler and echo together

Stepping back from a firecracker is not enough on its own

How far away was that earthquake?

Extend words to keep

Fourteen questions on Doppler shift, recording and wider contexts

Cheat sheet

Sources

What you just read

Explore a connection