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The Doppler Effect

The Doppler effect is the change in the frequency we hear (or detect) when the source of a wave and the observer move toward or away from each other. Moving closer squeezes the crests together: shorter wavelength, higher frequency, higher pitch. Moving apart stretches them: longer wavelength, lower frequency. For sound, f′ = f × (v ± vo) ÷ (v ∓ vs), using the upper signs when they approach. It is used in speed guns, weather radar, ultrasound scans of blood flow, bat echolocation and in astronomy (red shift and blue shift of light).

🎬 Step-by-step story

  1. A siren at rest sends out sound crests in circles. The gap between crests is the same on every side, so everyone hears the same pitch.
  2. Now the siren moves. Each new crest starts from a new place, so crests bunch up in front and spread out behind.
  3. In front, the crests are closer. More reach your ear each second, so you hear a higher pitch.
  4. Behind, the crests are further apart. Fewer reach your ear each second, so you hear a lower pitch.
  5. If the siren is still and you run toward it, you meet the crests more often. The pitch goes up again.
  6. Your turn: change the speeds and the frequency, predict the pitch, then check.

Tip: drag the 3D scene to turn it. Use two fingers to zoom.

🤔 Common doubts, cleared

Does the siren itself change its note?

No. Its frequency stays the same. Look at step 1: with the siren at rest, both ears get the same gap between crests.

Does the sound travel faster in front of a moving siren?

No. Every ring grows at the same speed. Only the starting point of each ring moves, so the gaps change, not the speed.

Why does a shorter wavelength mean a higher pitch?

The speed is fixed, so if crests are closer, more of them pass your ear each second. More crests per second is a higher frequency, which we hear as a higher pitch.

Why does the pitch drop only after it passes, not slowly?

Before passing, the siren moves toward you; after passing, away. The switch happens at the moment it passes, so the pitch drops quickly then.

Does it work if I move instead of the source?

Yes. Running toward a still source makes you meet crests more often, so the frequency rises even though the wavelength is the same.

What happens if the source goes as fast as sound?

The crests in front pile on top of each other and make a shock wave: a sonic boom. Push the siren speed slider high to see the front crests crowd together.

What is the Doppler effect?

A wave has a frequency f (crests sent out per second) and a wavelength λ (the gap between crests). For sound, a high frequency sounds like a high pitch.

The Doppler effect is the change in frequency an observer notices when the source and the observer move toward or away from each other. Toward: higher frequency. Away: lower frequency. It is named after Christian Doppler, who described it in 1842.

The source itself does not change. The siren still makes the same note. Only what reaches you changes.

Why it happens: crests bunch up and spread out

Moving source

Sound moves through air at speed v (about 340 m/s). The source sends one crest every 1/f seconds. If the source moves forward at speed vs, it chases its own crests. Each new crest starts a little closer to the one before. So in front: λ′ = (v − vs) ÷ f, shorter. Behind: λ′ = (v + vs) ÷ f, longer. The speed of sound is unchanged, so the heard frequency f′ = v ÷ λ′ changes.

Moving observer

If the source is still but you move toward it at speed vo, the wavelength does not change, but you run into crests faster: f′ = f × (v + vo) ÷ v. Moving away gives f′ = f × (v − vo) ÷ v.

Only the motion along the line joining source and observer counts. A car passing at the side gives the biggest change just before and just after it passes.

The Doppler formula for sound

f′ = f × (v ± vo) ÷ (v ∓ vs)

Sign rule: use the sign that makes f′ bigger when they move closer. Top signs (+vo, −vs) for moving toward each other; bottom signs (−vo, +vs) for moving apart.

Check with the 3D: siren at 120 m/s, f = 500 Hz. In front f′ = 500 × 340 ÷ 220 ≈ 773 Hz. Behind f′ = 500 × 340 ÷ 460 ≈ 370 Hz.

Limits: if vs reaches v, crests pile up into a shock wave (the sonic boom of a jet). The formula also assumes still air; wind changes the result.

Doppler effect for light: red shift and blue shift

Light is a wave too. When a star or galaxy moves away from us, its light is stretched to longer wavelength: a red shift. Moving toward us: blue shift. For speeds much less than light speed c, the fractional change is Δλ ÷ λ ≈ v ÷ c. Astronomers use this to measure how fast stars move, to find planets that make their star wobble, and to show that distant galaxies are moving away (the expanding universe).

Applications of the Doppler effect

Try it at home

Put a phone playing a steady beep (a tone generator app, 1000 Hz) in a sock and swing it in a circle on a string, safely away from people. A friend standing a few metres away hears the pitch go up and down every turn. Or stand by a road and listen to a horn as a vehicle passes. Predict first: when is the pitch highest?

Key formulas and definitions

Worked examples

1. An ambulance siren is 700 Hz. It drives toward you at 20 m/s. v = 340 m/s. What do you hear?

f′ = f × v ÷ (v − vs) = 700 × 340 ÷ 320 = 743.75 ≈ 744 Hz (higher).

2. The same ambulance now drives away at 20 m/s. What do you hear?

f′ = 700 × 340 ÷ 360 ≈ 661 Hz (lower).

3. You cycle at 10 m/s toward a still factory hooter of 510 Hz. v = 340 m/s.

f′ = f × (v + vo) ÷ v = 510 × 350 ÷ 340 = 525 Hz.

4. A 500 Hz source moves at 40 m/s toward you. Find the wavelength in front of it. v = 340 m/s.

λ′ = (v − vs) ÷ f = 300 ÷ 500 = 0.60 m. Without motion it would be 340 ÷ 500 = 0.68 m.

5. Before a train passes you hear its horn at 600 Hz; after it passes, 500 Hz. Find the train's speed. v = 340 m/s.

600 = f × 340 ÷ (340 − vs) and 500 = f × 340 ÷ (340 + vs). Divide: 600/500 = (340 + vs) ÷ (340 − vs). So 1.2(340 − vs) = 340 + vs → 408 − 1.2vs = 340 + vs → 68 = 2.2vs → vs ≈ 30.9 m/s.

6. A car (source, 400 Hz) and a bike (observer) move toward each other, car at 30 m/s, bike at 10 m/s. v = 340 m/s.

f′ = f × (v + vo) ÷ (v − vs) = 400 × 350 ÷ 310 ≈ 452 Hz.

Common mistakes

Practice quiz

1. As a siren comes toward you, its pitch sounds:
2. In front of a moving source, the wavelength is:
3. Which formula is for a source moving away from a still observer?
4. Light from a galaxy moving away from us shows:
5. Which device uses the Doppler effect?

Practice: answer these yourself

Type or choose your answer, then press Check. Use a hint if you are stuck; the full solution appears after you answer.

Frequently asked questions

What is the Doppler effect in simple words?

It is the change in pitch (frequency) you hear when a sound source and you move toward or away from each other. Closer means higher, apart means lower.

What is the Doppler effect formula?

For sound, f′ = f × (v ± vo) ÷ (v ∓ vs). Use the signs that make f′ larger when the source and observer approach each other.

Where is the Doppler effect used?

In police speed guns, weather radar, Doppler ultrasound scans, bat echolocation, satellite tracking and astronomy (red shift and blue shift).

Where this is taught

South Korea고등학교 2학년Elastic waves and sound
South Korea고등학교 3학년Waves and properties of matter
China高二Selective 1 Ch.3 Mechanical waves

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