Final answer:
The speed of the ambulance can be calculated using the Doppler Effect formula, × vs = v × ((fs - fo) / fo),× where fo is the observed frequency, fs is the source frequency, vs is the speed of the source, and v is the speed of sound.
Step-by-step explanation:
To determine the speed of the ambulance based on the observed frequency and the actual frequency of the siren, we can use the Doppler Effect equation. The Doppler Effect describes the change in frequency of a wave in relation to an observer who is moving relative to the wave source. In this case, the ambulance is the source, and the student is the observer.
The formula for the Doppler Effect when the source is moving towards a stationary observer is:
fo = (v / (v - vs)) × fs
Where:
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- fo is the observed frequency (415 Hz)
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- fs is the source frequency (395 Hz)
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- vs is the speed of the source (ambulance)
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- v is the speed of sound (343 m/s)
Using this equation, we can solve for the ambulance's speed (vs) by rearranging the formula:
vs = v × ((fs - fo) / fo)
Plugging in the values:
vs = 343 m/s × ((395 Hz - 415 Hz) / 415 Hz)
This procedure helps find the speed at which the ambulance is moving towards the observer.