Final answer:
The frequency received by a person as an oncoming ambulance approaches at 110 km/h is approximately 877.8 Hz, and after the ambulance has passed, it is approximately 734.4 Hz, calculated by applying the Doppler Effect.
Step-by-step explanation:
To calculate the frequency received by a person watching an oncoming ambulance with the given parameters, we must apply the Doppler Effect formula. The formula for the frequency received by an observer when the source of sound is moving toward the observer is:
f' = f * (v + vo) / (v - vs)
where:
- f' is the frequency observed by the observer.
- f is the emitted frequency of the source (800 Hz in this case).
- v is the speed of sound (345 m/s on this day).
- vo is the speed of the observer (0 m/s as they are stationary).
- vs is the speed of the source, the ambulance (110 km/h which needs to be converted to m/s).
First, we convert the ambulance's speed from km/h to m/s:
110 km/h = (110 * 1000 m) / (3600 s) = 30.55 m/s
Now we can plug the values into the formula:
f' = 800 Hz * (345 m/s + 0 m/s) / (345 m/s - 30.55 m/s) = 800 Hz * 345 m/s / 314.45 m/s
Calculating the above gives us:
f' ≈ 800 Hz * 1.097 ≈ 877.8 Hz
Therefore, the frequency received by the person as the ambulance approaches is approximately 877.8 Hz.
For the second part of the question:
When the ambulance has passed, the formula changes slightly to account for the source moving away from the observer:
f' = f * (v - vo) / (v + vs)
Since the observer's speed and the calculation of the ambulance's speed remain the same, we substitute these values back into the formula:
f' = 800 Hz * (345 m/s - 0) / (345 m/s + 30.55 m/s) = 800 Hz * 345 m/s / 375.55 m/s
This calculation gives:
f' ≈ 800 Hz * 0.918 ≈ 734.4 Hz
So, after the ambulance has passed, the frequency received by the person is approximately 734.4 Hz.