A car moves at a constant velocity of 22 m.s⁻¹ on a straight horizontal road TOWARDS a stationary device, which can both emit and detect sound waves. The device emits sound waves with a frequency of 24 000 Hz. These sound waves are reflected off the car and the reflected sound waves are then detected by the device, as shown in the diagram below. 6.1.1 State the Doppler effect in words. 6.1.2 If the speed of sound in air is 340 m.s⁻¹, calculate the frequency of the reflected sound waves detected by the device.

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

A car moves at a constant velocity of 22 m.s⁻¹ on a straight horizontal road TOWARDS a stationary device, which can both emit and detect sound waves - NSC Physical Sciences - Question 6 - 2023 - Paper 1

Question 6

A-car-moves-at-a-constant-velocity-of-22-m.s⁻¹-on-a-straight-horizontal-road-TOWARDS-a-stationary-device,-which-can-both-emit-and-detect-sound-waves-NSC Physical Sciences-Question 6-2023-Paper 1.png

A car moves at a constant velocity of 22 m.s⁻¹ on a straight horizontal road TOWARDS a stationary device, which can both emit and detect sound waves. The device emi... show full transcript

Worked Solution & Example Answer:A car moves at a constant velocity of 22 m.s⁻¹ on a straight horizontal road TOWARDS a stationary device, which can both emit and detect sound waves - NSC Physical Sciences - Question 6 - 2023 - 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 a sound detected by a listener, due to the relative motion between a source of sound and the observer. As the source approaches the observer, the frequency appears to increase, and as it moves away, the frequency appears to decrease.

Step 2

If the speed of sound in air is 340 m.s⁻¹, calculate the frequency of the reflected sound waves detected by the device.

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Answer

To calculate the frequency of the reflected sound waves detected by the device, we use the Doppler effect formula. The formula for the observed frequency is:

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

Where:

$f_l$ is the observed frequency.
$f_s$ is the source frequency = 24000 Hz.
$v$ is the speed of sound = 340 m.s⁻¹.
$v_L$ is the velocity of the listener (device) = 0 m.s⁻¹ (since the device is stationary).
$v_s$ is the velocity of the source (car) = 22 m.s⁻¹.

Substituting the values:

$f_l = 24000 \frac{340 + 0}{340 - 22}$ $f_l = 24000 \frac{340}{318}$ Calculating further gives: $f_l \approx 25225.68 \text{ Hz}$

Thus, the frequency of the reflected sound waves detected by the device is approximately 25226 Hz.

A car moves at a constant velocity of 22 m.s⁻¹ on a straight horizontal road TOWARDS a stationary device, which can both emit and detect sound waves - NSC Physical Sciences - Question 6 - 2023 - Paper 1

Worked Solution & Example Answer:A car moves at a constant velocity of 22 m.s⁻¹ on a straight horizontal road TOWARDS a stationary device, which can both emit and detect sound waves - NSC Physical Sciences - Question 6 - 2023 - Paper 1

State the Doppler effect in words.

If the speed of sound in air is 340 m.s⁻¹, calculate the frequency of the reflected sound waves detected by the device.

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