A car is approaching you at a speed of 30 m/s while sounding its horn, which emits a constant frequency of 500 Hz. Calculate the frequency of the sound you hear when the car is 100 meters away from you.
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To calculate the frequency of the sound you hear, we can use the Doppler effect formula:
f' = f * (v + v₀) / (v + vᵢ)
where:
- f' is the observed frequency
- f is the emitted frequency
- v is the speed of sound in air (approximately 343 m/s)
- v₀ is the velocity of the observer (you)
- vᵢ is the velocity of the source (car)
Given:
- f = 500 Hz
- v = 343 m/s
- v₀ = 0 m/s (since you are at rest)
- vᵢ = 30 m/s
Plugging the values into the formula:
f' = 500 * (343 + 0) / (343 + 30)
f' = 500 * 343 / 373
f' ≈ 458 Hz
Therefore, the frequency of the sound you hear when the car is 100 meters away from you is approximately 458 Hz.
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