A car moves at a constant speed of 10 m s⁻¹ TOWARDS a stationary sound source. The sound source emits sound waves of frequency 880 Hz. A sound detector A is attached to the car and another sound detector B is attached to the sound source. Detector B detects the sound waves reflected from the car. The speed of sound in air is 340 m s⁻¹: 6.1 State the Doppler effect in words. 6.2 Calculate the wavelength of the sound waves emitted by the source. 6.3 Calculate the frequency of the sound waves detected by detector A. The sketch graph below shows the frequency recorded by detector A. 6.4 Redraw the graph above for detector A in your ANSWER BOOK. On the same set of axes, sketch the graph of the frequency recorded by detector B. Label this graph as B.

NSC Physical Sciences Doppler Effect: A car moves at a constant speed

A car moves at a constant speed of 10 m s⁻¹ TOWARDS a stationary sound source - NSC Physical Sciences - Question 6 - 2022 - Paper 1

Question 6

A car moves at a constant speed of 10 m s⁻¹ TOWARDS a stationary sound source. The sound source emits sound waves of frequency 880 Hz. A sound detector A is attache... show full transcript

Worked Solution & Example Answer:A car moves at a constant speed of 10 m s⁻¹ TOWARDS a stationary sound source - NSC Physical Sciences - Question 6 - 2022 - Paper 1

Step 1

6.1 State the Doppler effect in words.

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Answer

The Doppler effect is the apparent change in frequency (or pitch) of sound waves as perceived by an observer moving relative to the source of the sound. This occurs because the source and observer are moving at different velocities relative to the medium through which the sound is propagating.

Step 2

6.2 Calculate the wavelength of the sound waves emitted by the source.

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Answer

To find the wavelength $ext{λ}$ of the sound waves emitted by the source, we use the formula:

$v = f imes ext{λ}$

Where:

$v$ is the speed of sound in air (340 m s⁻¹)
$f$ is the frequency of the sound (880 Hz)

Rearranging gives us:

$ext{λ} = \frac{v}{f} = \frac{340}{880} = 0.386 \text{ m}$

Step 3

6.3 Calculate the frequency of the sound waves detected by detector A.

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Answer

To calculate the frequency detected by detector A ( $f_A$ ), we can use the Doppler effect formula:

$f_A = f_s \frac{v + v_L}{v - v_S}$

Where:

$v$ is the speed of sound (340 m s⁻¹)
$f_s$ is the frequency of the source (880 Hz)
$v_L$ is the speed of the listener (10 m s⁻¹ towards the source)
$v_S$ is the speed of the source (0 m s⁻¹ since it is stationary)

Plugging in the values gives:

$f_A = 880 \frac{340 + 10}{340 - 0} = 905.88 \text{ Hz}$

Step 4

6.4 Redraw the graph above for detector A in your ANSWER BOOK. On the same set of axes, sketch the graph of the frequency recorded by detector B. Label this graph as B.

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Answer

In this task, you should sketch two graphs on the same axes:

The graph for detector A will show a frequency that increases as the car approaches the sound source and then decreases as the car moves away.
The graph for detector B will remain at a constant frequency of 880 Hz since the sound source is stationary. Make sure to label the axes with time (s) on the horizontal and frequency (Hz) on the vertical. Label the curve for detector A and the horizontal line for detector B.

A car moves at a constant speed of 10 m s⁻¹ TOWARDS a stationary sound source - NSC Physical Sciences - Question 6 - 2022 - Paper 1

Worked Solution & Example Answer:A car moves at a constant speed of 10 m s⁻¹ TOWARDS a stationary sound source - NSC Physical Sciences - Question 6 - 2022 - Paper 1

6.1 State the Doppler effect in words.

6.2 Calculate the wavelength of the sound waves emitted by the source.

6.3 Calculate the frequency of the sound waves detected by detector A.

6.4 Redraw the graph above for detector A in your ANSWER BOOK. On the same set of axes, sketch the graph of the frequency recorded by detector B. Label this graph as B.

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