Doppler effect for sound waves

General physics

🎯 Learning Objectives

Explain how the Doppler effect changes observed frequency when a sound source moves relative to a stationary observer
Recall and use the formula f_o = f_s v / (v ± v_s) for a moving source and stationary observer
Sketch and interpret frequency vs source-speed graphs for approaching and receding sources
Calculate observed frequency for given source speeds and sound speed

🗣️ Language Objectives

Use terms “Doppler effect,” “stationary observer,” “source frequency,” “observed frequency” accurately
Explain formula components and reasoning in clear English
Describe changes in pitch using precise academic vocabulary
Interpret problem statements and communicate solutions effectively

📚 Key Terms and Translations

English Term	Russian	Kazakh
Doppler effect	Эффект Доплера	Доплер әсері
Source frequency (f_s)	Частота источника (f_s)	Дереккөз жиілігі (f_s)
Observed frequency (f_o)	Наблюдаемая частота (f_o)	Бақыланған жиілік (f_o)
Stationary observer	Неподвижный наблюдатель	Тірексіз бақылаушы
Source speed (v_s)	Скорость источника (v_s)	Дереккөз жылдамдығы (v_s)
Wave speed (v)	Скорость волны (v)	Толқын жылдамдығы (v)

🃏 Vocabulary Study Cards

Doppler Effect

Definition: Change in observed frequency due to relative motion between source and observer.

Example: Siren pitch rises as ambulance approaches.

Stationary Observer

Definition: An observer at rest relative to the medium through which sound travels.

Key Point: Only the source moves in our formula.

Source Frequency

Symbol: f_s

Meaning: Frequency emitted by the source in its rest frame.

Observed Frequency

Symbol: f_o

Meaning: Frequency measured by the stationary observer.

📖 Glossary of Terms

Doppler effect

The change in frequency or wavelength of a wave in relation to an observer moving relative to the wave source.

Translation

Russian: Изменение частоты или длины волны для наблюдателя, движущегося относительно источника.
Kazakh: Қозғалатын бақылаушы үшін толқынның жиілігінің немесе ұзындығының өзгеруі.
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Stationary observer

An observer at rest with respect to the medium in which the wave propagates; only the source moves.

Translation

Russian: Наблюдатель, неподвижный относительно среды распространения волны.
Kazakh: Толқынды тасымалдайтын ортаға қатысты қозғалмайтын бақылаушы.
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🔬 Theory: Doppler Effect for Sound Waves

For a sound wave emitted by a source moving at speed v_s relative to a observer at rest, the observed <su_tooltip text="частота/жиілік" behavior="click"]frequency[/su_tooltip] f_o is given by:

f_o = f_s × v / (v − v_s) when the source approaches,

f_o = f_s × v / (v + v_s) when the source recedes.

Translation

Russian: Для звуковой волны от источника, движущегося со скоростью v_s относительно неподвижного наблюдателя, наблюдаемая частота определяется как f_o = f_s·v/(v–v_s) при сближении и f_o = f_s·v/(v+v_s) при удалении.
Kazakh: Қозғалатын дереккөздің жылдамдығы v_s бар дыбыс толқыны үшін тірексіз бақылаушыдағы жиілік f_o = f_s·v/(v–v_s) жақындағанда және f_o = f_s·v/(v+v_s) алшақтағанда есептеледі.
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Theory Questions

Easy: Describe qualitatively why a siren’s pitch changes as it passes you.

Answer

As the ambulance approaches, wavefronts compress, increasing frequency; as it recedes, they stretch, lowering frequency.

Medium: Write down the Doppler formula for a moving source and define each symbol.

Answer

f_o=f_s·v/(v±v_s): f_o=observed frequency, f_s=source frequency, v=wave speed, v_s=source speed.

Medium: A 500 Hz source moves towards you at 20 m/s in air (v=343 m/s). Calculate f_o.

Answer

f_o=500·343/(343–20)≈500·343/323≈530 Hz.

Hard (Critical Thinking): Discuss why the formula breaks down as v_s→v and what phenomenon occurs.

Answer

As v_s approaches v, denominator →0, predicted f_o→∞. In reality a shock wave (sonic boom) forms.

💪 Memorization Exercises

Fill in the Blanks

The Doppler formula for a moving source is f_o=f_s·v/(v ± ___).
When the source moves towards the observer, use the ___ sign in the denominator.
As v_s→v, the predicted f_o→___.
Sonic boom occurs when the source speed exceeds ___.

Answer

1. v_s
2. minus (–)
3. infinity
4. wave speed (v)

🎥 Video Lesson

Additional Video Resources:

• Cambridge A-Level Examples of Doppler Effect

• AS Waves: Doppler Effect

📐 Worked Examples

Example 1: Approaching Source

A 400 Hz train horn approaches at 15 m/s. Calculate observed frequency (v=343 m/s).

Doppler approaching diagram

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Example 2: Receding Source

A 600 Hz siren recedes at 25 m/s. Find f_o (v=343 m/s).

Solution

Answer

f_o=400·343/(343–15)≈400·343/328≈418 Hz.

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🧪 Interactive Investigation

Use PhET “Sound” simulation to explore Doppler shifts by moving the source and microphone:

Investigation Answers

1. Move the speaker towards the microphone; record higher f_o.
2. Move it away; record lower f_o.
3. Compare measured values to f_s·v/(v±v_s).

👥 Collaborative Group Activity

In small groups, use this Quizizz challenge on Doppler effect:

📝 Individual Assessment

Solve these structured questions:

Derive f_o=f_s·v/(v±v_s) from wavefront geometry.
A fire engine (700 Hz) approaches at 30 m/s. Calculate f_o and discuss error sources.
Sketch f_o vs v_s for v_s from 0 to 300 m/s.
Explain qualitatively what happens when v_s>v (supersonic source).
Design an experiment using smartphone apps to measure Doppler shift of moving vehicles.

🔗 Additional Learning Resources

🤔 Lesson Reflection

Which case (approaching vs receding) gave you larger frequency shift? Why?
How sensitive is f_o to small changes in v_s?
What practical challenges arise in measuring Doppler shifts in air?
How might the Doppler effect be used in medical ultrasound or radar?