The Doppler Effect with Sound Revision Notes for Grade 12 NSC Matric Physical Sciences

The Doppler Effect with Sound

What is the Doppler effect?

The Doppler effect occurs when there is relative motion between a wave source and an observer. This phenomenon is commonly experienced when you hear an ambulance or train approaching - the pitch sounds higher as it comes towards you and lower as it moves away.

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Definition: The Doppler effect is the change in the observed frequency of a wave when the source or the detector moves relative to the transmitting medium.

Key terms

Observer (or listener): The person or device detecting the sound waves
Source: The object emitting the sound waves
Relative motion: Movement between the source and observer

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The Doppler effect occurs in two main situations:

When the source moves relative to a stationary observer
When the observer moves relative to a stationary source

Case 1: Moving source, stationary observer

When a sound source remains stationary, it emits waves as concentric circles spreading outward in all directions. The distance between consecutive wave crests (wavelength) remains constant.

However, when the source starts moving, something interesting happens. As the source moves, it emits new wave crests while the previous ones continue spreading outward. This creates a pattern where:

In front of the moving source: Wave crests become bunched together (shorter wavelength, higher frequency)
Behind the moving source: Wave crests become spread apart (longer wavelength, lower frequency)

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Key Insight: The source's motion changes the spacing between wave crests, which directly affects the frequency an observer detects.

What you hear

When a car approaches you: The sound waves reaching you have a shorter wavelength and higher frequency, so you hear a higher pitch
When the car moves away from you: The sound waves reaching you have a longer wavelength and lower frequency, so you hear a lower pitch

This explains why an ambulance siren changes pitch as it passes by - it's higher when approaching and lower when moving away.

Case 2: Moving observer, stationary source

Now consider the situation where the source (like a police car) is stationary, but the observers are moving.

The frequency an observer measures depends on how many complete wave cycles they encounter per unit time.

How motion affects what you hear

Observer moving towards the source: Encounters more wave crests per unit time, measuring a higher frequency
Observer moving away from the source: Encounters fewer wave crests per unit time, measuring a lower frequency

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Key Insight: Motion between source and observer changes the frequency detected, even though the source continues emitting at its original frequency.

The Doppler effect formula

The mathematical relationship between the source frequency and observed frequency is:

$f_L = \frac{v \pm v_L}{v \pm v_S} \times f_S$

Where:

$f_L$ = frequency perceived by the observer (listener)
$f_S$ = frequency of the source
$v$ = speed of sound waves
$v_L$ = speed of the listener
$v_S$ = speed of the source

Sign conventions

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Critical Sign Rules:

Source moves towards listener: $v_S$ is negative
Source moves away from listener: $v_S$ is positive
Listener moves towards source: $v_L$ is positive
Listener moves away from source: $v_L$ is negative

Memory tip

Think of it this way: when source and observer move towards each other, you get addition effects that increase frequency. When they move apart, you get subtraction effects that decrease frequency.

Worked example 1: Ambulance siren

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Worked Example: Ambulance Siren Frequency Change

Question: An ambulance siren emits sound at 700 Hz. You are standing on the pavement. If the ambulance drives past at 20 m·s⁻¹, what frequency do you hear when: a) The ambulance approaches you b) The ambulance moves away from you

Take the speed of sound as 340 m·s⁻¹.

Solution:

Step 1: Analyse the question This is a moving source problem. The observer (you) is stationary, so $v_L = 0$ .

Step 2: Identify the given values

$f_S = 700$ Hz
$v = 340$ m·s⁻¹
$v_L = 0$ (stationary observer)
$v_S = -20$ m·s⁻¹ (approaching) or $+20$ m·s⁻¹ (moving away)

Step 3: Calculate $f_L$ when ambulance approaches

$f_L = \frac{v \pm v_L}{v \pm v_S} \times f_S$

$f_L = \frac{340 + 0}{340 - 20} \times 700 = \frac{340}{320} \times 700 = 743.75 \text{ Hz}$

Step 4: Calculate $f_L$ when ambulance moves away

$f_L = \frac{340 + 0}{340 + 20} \times 700 = \frac{340}{360} \times 700 = 661.11 \text{ Hz}$

Answer: When approaching: 743.75 Hz; When moving away: 661.11 Hz

Worked example 2: Moving observer

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Worked Example: Moving Observer Frequency

Question: What frequency does a person driving at 15 m·s⁻¹ towards a factory whistle hear if the whistle blows at 800 Hz? Assume the speed of sound is 340 m·s⁻¹.

Solution:

Step 1: Analyse the question This is a moving observer problem. The source is stationary, so $v_S = 0$ .

Step 2: Identify values

$v = 340$ m·s⁻¹
$v_L = +15$ m·s⁻¹ (moving towards source)
$v_S = 0$ m·s⁻¹ (stationary source)
$f_S = 800$ Hz

Step 3: Calculate the frequency

$f_L = \frac{v \pm v_L}{v \pm v_S} \times f_S$

$f_L = \frac{340 + 15}{340 + 0} \times 800 = \frac{355}{340} \times 800 = 835.29 \text{ Hz}$

Answer: The driver hears a frequency of 835.29 Hz.

Worked example 3: Train approaching station

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Worked Example: Train Station Scenario

Question: A train approaches a station at 20 m·s⁻¹ with its whistle blowing at 458 Hz. An observer on the platform hears a change in pitch as the train approaches, passes, and moves away.

Name the phenomenon that explains the change in pitch (1 mark)
Calculate the frequency heard while the train approaches (4 marks)
How will the frequency change as the train moves away? (1 mark)

Solution:

Question 1: Doppler effect (1 mark)

Question 2: Calculate approach frequency

$f_L = \frac{v \pm v_L}{v \pm v_S} \times f_S$

$f_L = \frac{340 + 0}{340 - 20} \times 458 = \frac{340}{320} \times 458 = 486.63 \text{ Hz}$ (4 marks)

Question 3: The frequency decreases (1 mark)

Real-world applications: Ultrasound and medical diagnosis

The Doppler effect has important applications in medicine. Ultrasound devices use sound waves with frequencies greater than 20,000 Hz to examine blood flow in the body.

How medical Doppler works

Sound waves are sent into the body and reflected by moving blood cells
Blood moving towards the detector reflects waves at a higher frequency
Blood moving away from the detector reflects waves at a lower frequency
The frequency shift indicates blood flow speed and direction

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This technique, called sonography or ultrasonography, helps doctors detect:

Blocked arteries
Blood flow problems
Heart valve issues
Circulation problems in unborn babies

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Key Points to Remember:

The Doppler effect changes the observed frequency when there is relative motion between source and observer
Approaching motion (source and observer moving towards each other) produces higher frequency
Receding motion (source and observer moving apart) produces lower frequency
Use the formula $f_L = \frac{v \pm v_L}{v \pm v_S} \times f_S$ with correct sign conventions
The effect has important applications in medical diagnosis using ultrasound technology

The Doppler Effect with Sound (Grade 12 NSC Matric Physical Sciences): Revision Notes