Answer :
The frequency detected by the moving observer is approximately 1772.69 Hz.
When a sound source is moving towards a stationary observer, the frequency of the sound waves detected by the observer is higher than the frequency emitted by the source. This is known as the Doppler effect.
The formula for the Doppler effect is:
f' = (v ± vo) / (v ± vs) * f
where:
f = frequency emitted by the source
f' = frequency detected by the observer
v = speed of sound in air (approximately 343 m/s at room temperature)
vo = speed of the observer relative to the air
vs = speed of the source relative to the air
In this case, the source is the fire engine and the observer is someone who is moving towards the fire engine with a speed of 37.1 m/s.
Given that the predominant frequency of the siren when at rest is 1570 Hz, we can use the Doppler effect formula to calculate the frequency detected by the moving observer.
First, we need to determine the speed of the fire engine relative to the air. Since this information is not given, we'll assume that the fire engine is at rest relative to the air.
Using the formula above, we have:
f' = (v + vo) / (v + vs) * f
where:
f = 1570 Hz
v = 343 m/s
vo = 37.1 m/s (since the observer is moving towards the fire engine)
vs = 0 m/s (since the fire engine is assumed to be at rest relative to the air)
Substituting the values, we get:
f' = (343 + 37.1) / (343 + 0) * 1570
f' = 1.129 * 1570
f' = 1772.69 Hz
Therefore, the frequency detected by the moving observer is approximately 1772.69 Hz.
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