The siren of a stationary ambulance emits sound waves at a constant frequency of 680 Hz. A man is standing with a detector that records the wavelength of the sound emitted by the siren, as shown in the diagram. The speed of sound in air is 340 m s⁻¹. 6.1 Calculate the wavelength of the detected sound. The ambulance now moves at a constant speed along the road TOWARDS the man. The detector now records the wavelength of the sound, which differs from the previous reading by 0,05 m. 6.2 State the Doppler effect. 6.3 How would EACH of the following have changed when the ambulance approached the detector compared to when the ambulance was stationary? Choose from INCREASED, DECREASED or NO CHANGE. 6.3.1 Distance between the wave fronts 6.3.2 Frequency of the detected waves 6.4 Calculate the speed of the ambulance.

NSC Physical Sciences Doppler Effect: The siren of a stationary ambula

The siren of a stationary ambulance emits sound waves at a constant frequency of 680 Hz - NSC Physical Sciences - Question 6 - 2021 - Paper 1

Question 6

The siren of a stationary ambulance emits sound waves at a constant frequency of 680 Hz. A man is standing with a detector that records the wavelength of the sound e... show full transcript

Worked Solution & Example Answer:The siren of a stationary ambulance emits sound waves at a constant frequency of 680 Hz - NSC Physical Sciences - Question 6 - 2021 - Paper 1

Step 1

6.1 Calculate the wavelength of the detected sound.

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Answer

To calculate the wavelength ( λ ), we can use the formula relating speed (

v ), frequency (

f ), and wavelength:

v = f \cdot \lambda$$ Given that the speed of sound in air is 340 m/s and the frequency is 680 Hz, we rearrange the equation to solve for wavelength: $$\lambda = \frac{v}{f} = \frac{340 \, \text{m/s}}{680 \, \text{Hz}} = 0.5 \, \text{m}$$ Thus, the wavelength of the detected sound is 0.5 m.

Step 2

6.2 State the Doppler effect.

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Answer

The Doppler effect refers to the change in frequency (or pitch) of a wave in relation to an observer who is moving relative to the wave source. When the source of the sound moves towards the observer, the observed frequency increases; when it moves away, the observed frequency decreases.

Step 3

6.3.1 Distance between the wave fronts

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Answer

DECREASED

Step 4

6.3.2 Frequency of the detected waves

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Answer

INCREASED

Step 5

6.4 Calculate the speed of the ambulance.

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Answer

When the ambulance approaches the detector, the new wavelength recorded is 0.45 m (0.5 m - 0.05 m). The new frequency can be calculated using:

$f' = \frac{v}{\lambda'} = \frac{340 \, \text{m/s}}{0.45 \, \text{m}} \approx 755.56 \, \text{Hz}$

Using the Doppler effect relationship, we can find the speed of the ambulance: $f' = f \frac{v + v_s}{v - v_s}$ Where:

$f'$ is the observed frequency (755.56 Hz)
$f$ is the source frequency (680 Hz)
$v$ is the speed of sound (340 m/s)
$v_s$ is the speed of the ambulance (unknown)

Rearranging the formula gives: $755.56 = 680 \frac{340 + v_s}{340 - v_s}$

Solving for $v_s$ yields:

Cross-multiply and simplify the equation.
Solve for $v_s$ . The speed of the ambulance is approximately 34 m/s.

The siren of a stationary ambulance emits sound waves at a constant frequency of 680 Hz - NSC Physical Sciences - Question 6 - 2021 - Paper 1

Worked Solution & Example Answer:The siren of a stationary ambulance emits sound waves at a constant frequency of 680 Hz - NSC Physical Sciences - Question 6 - 2021 - Paper 1

6.1 Calculate the wavelength of the detected sound.

6.2 State the Doppler effect.

6.3.1 Distance between the wave fronts

6.3.2 Frequency of the detected waves

6.4 Calculate the speed of the ambulance.

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