6.1 A police car is moving at constant velocity on a freeway. The siren of the car emits sound waves with a frequency of 330 Hz. A stationary sound detector measures the frequency of the sound waves of the approaching siren as 365 Hz. Take the speed of sound in air as 340 m·s⁻¹. 6.1.1 State the Doppler Effect in words. 6.1.2 Calculate the speed of the car. 6.2 The spectrum of a distant star when viewed from an observatory on Earth appears to have undergone a red shift. Use your knowledge of the Doppler effect to explain the term red shift.

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6.1 A police car is moving at constant velocity on a freeway - NSC Physical Sciences - Question 6 - 2017 - Paper 1

Question 6

6.1 A police car is moving at constant velocity on a freeway. The siren of the car emits sound waves with a frequency of 330 Hz. A stationary sound detector measures... show full transcript

Worked Solution & Example Answer:6.1 A police car is moving at constant velocity on a freeway - NSC Physical Sciences - Question 6 - 2017 - Paper 1

Step 1

State the Doppler Effect in words.

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Answer

The Doppler Effect is defined as the change in frequency (or pitch) of the sound detected by a listener because the sound source and the listener have different velocities relative to the medium of sound propagation. It is an apparent change in frequency (or wavelength) due to the relative motion between a source and an observer.

Step 2

Calculate the speed of the car.

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Answer

Using the Doppler Effect formula:

$f_s = f_t \frac{v + v_L}{v - v_s}$

Where:

$f_s$ is the frequency of the source (siren) = 330 Hz
$f_t$ is the frequency detected = 365 Hz
$v$ is the speed of sound = 340 m/s
$v_L$ is the speed of the listener (0 for stationary)
$v_s$ is the speed of the source (car)

Plugging in the values:

$365 = 330 \frac{340 + 0}{340 - v_s}$

Rearranging gives:

$365(340 - v_s) = 330 \times 340$

Solving for $v_s$ :

$365 \times 340 - 365 v_s = 112200$

$124100 - 112200 = 365v_s$

$v_s = \frac{11900}{365} \approx 32.6 \, m/s$ .

Therefore, the speed of the car is approximately 32.6 m/s.

Step 3

Use your knowledge of the Doppler effect to explain the term red shift.

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Answer

The term 'red shift' refers to the phenomenon observed when an object in space, such as a distant star, moves away from the observer. According to the Doppler Effect, as the object recedes, the wavelengths of light it emits are stretched, resulting in a longer wavelength. This shift towards the red end of the spectrum indicates that the object is moving away from us, providing evidence for the expansion of the universe.

6.1 A police car is moving at constant velocity on a freeway - NSC Physical Sciences - Question 6 - 2017 - Paper 1

Worked Solution & Example Answer:6.1 A police car is moving at constant velocity on a freeway - NSC Physical Sciences - Question 6 - 2017 - Paper 1

State the Doppler Effect in words.

Calculate the speed of the car.

Use your knowledge of the Doppler effect to explain the term red shift.

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