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6.1 An ambulance is moving away from a stationary listener with a constant velocity of 25 m·s⁻¹ - NSC Physical Sciences - Question 6 - 2023 - Paper 1
Question 6
6.1 An ambulance is moving away from a stationary listener with a constant velocity of 25 m·s⁻¹. The siren of the ambulance emits sound waves at a frequency of 550 H... show full transcript
Worked Solution & Example Answer:6.1 An ambulance is moving away from a stationary listener with a constant velocity of 25 m·s⁻¹ - NSC Physical Sciences - Question 6 - 2023 - Paper 1
Step 1
State the Doppler effect in words.
Answer
The Doppler effect refers to the change in frequency (or wavelength) of a wave in relation to an observer moving relative to the wave source. When the source of sound is moving away from the observer, the observed frequency decreases, while if the source is moving towards the observer, the observed frequency increases.
Step 2
Use the given information to calculate the speed of sound in air.
Answer
To calculate the speed of sound in air, we can use the formula derived from the Doppler effect:
f' = rac{v + v_L}{v - v_S} f_S
where:
- is the frequency detected by the listener (512.64 Hz),
- is the speed of sound in air,
- is the velocity of the listener (0 m/s, as the listener is stationary),
- is the velocity of the source (25 m/s),
- is the frequency emitted by the source (550 Hz).
Rearranging the formula and solving for :
Substituting in the known values:
512.64 = rac{v}{v - 25} imes 550
This can be rearranged and solved to find:
Step 6
Step 7
Use the Doppler effect to explain the answer to QUESTION 6.2.1.
Answer
The red shift of the spectrum indicates that the wavelengths of light from the star are stretched, which occurs when the source of light is moving away from the observer. This shifting towards the red end of the spectrum is characteristic of an object receding, thus confirming that the star is moving away from the Earth.