A police car moving at a constant velocity with its siren on, passes a stationary listener. The graph below shows the changes in the frequency of the sound of the siren detected by the listener. 6.1 State the Doppler Effect in words. (2) 6.2 Write down the frequency of the sound detected by the listener as the police car: 6.2.1 Approaches the listener (1) 6.2.2 Moves away from the listener (1) 6.3 Calculate the speed of the police car. Take the speed of sound in air to be 340 m s⁻¹. (6)

NSC Physical Sciences Doppler Effect: A police car moving at a constan

A police car moving at a constant velocity with its siren on, passes a stationary listener - NSC Physical Sciences - Question 6 - 2017 - Paper 1

Question 6

A police car moving at a constant velocity with its siren on, passes a stationary listener. The graph below shows the changes in the frequency of the sound of the s... show full transcript

Worked Solution & Example Answer:A police car moving at a constant velocity with its siren on, passes a stationary listener - 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 the apparent change in frequency (or pitch) of sound detected by a listener due to the relative motion between the sound source and the listener. This effect occurs because the listener and the source are moving at different velocities relative to the medium through which the sound waves are propagating.

Step 2

Write down the frequency of the sound detected by the listener as the police car approaches the listener.

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Answer

170 Hz

Step 3

Write down the frequency of the sound detected by the listener as the police car moves away from the listener.

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Answer

130 Hz

Step 4

Calculate the speed of the police car. Take the speed of sound in air to be 340 m s⁻¹.

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Answer

To calculate the speed of the police car, we can use the Doppler effect formula:

$f_{t} = f_{s} \frac{v + v_{0}}{v - v_{s}}$

Where:

$f_{t}$ is the frequency detected by the listener (either 170 Hz or 130 Hz),
$f_{s}$ is the frequency of the source,
$v$ is the speed of sound (340 m s⁻¹),
$v_{0}$ is the speed of the listener (0 m s⁻¹, stationary),
$v_{s}$ is the speed of the source (police car).

For when the car approaches:

Using 170 Hz:

$170 = f_{s} \frac{340 + 0}{340 - v_{s}}$

And for when the car moves away:

Using 130 Hz:

$130 = f_{s} \frac{340 + 0}{340 + v_{s}}$

Solving these equations simultaneously will yield the speed of the police car, which calculates to approximately 45.35 m s⁻¹ (with a range of 45.35 m s⁻¹ to 45.45 m s⁻¹).

A police car moving at a constant velocity with its siren on, passes a stationary listener - NSC Physical Sciences - Question 6 - 2017 - Paper 1

Worked Solution & Example Answer:A police car moving at a constant velocity with its siren on, passes a stationary listener - NSC Physical Sciences - Question 6 - 2017 - Paper 1

State the Doppler Effect in words.

Write down the frequency of the sound detected by the listener as the police car approaches the listener.

Write down the frequency of the sound detected by the listener as the police car moves away from the listener.

Calculate the speed of the police car. Take the speed of sound in air to be 340 m s⁻¹.

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