A observer is standing 10 m from a road on which a vehicle is approaching him at a speed of 96 /hr when the vehicle is 50 m away from him, it blows a horn of frequency 8000 Hz what will be the frequency observed by the observer?Correct answer is '8668'. Can you explain this answer?

Question

Answer

Given:
- Distance between the observer and the road, d = 10 m
- Speed of the vehicle, v = 96 km/hr = 96 m/s
- Distance between the vehicle and the observer when the horn is blown, D = 50 m
- Frequency of the horn, f = 8000 Hz

Formula:
The observed frequency (f') of a sound wave emitted by a moving source can be calculated using the formula:

f' = f * (v + v₀) / (v + vₒ)

Where:
- f' is the observed frequency
- f is the actual frequency of the sound wave
- v is the speed of sound in air (approximately 343 m/s)
- v₀ is the speed of the observer relative to the medium (positive if the observer is moving towards the source, negative if moving away)

Calculation:
1. Convert the speed of the vehicle from km/hr to m/s:
v = 96 km/hr * (1000 m/km) * (1 hr/3600 s) = 26.67 m/s

2. Calculate the speed of the observer relative to the medium:
v₀ = v - 0 = 26.67 m/s - 0 m/s = 26.67 m/s (since the observer is stationary)

3. Substitute the values into the formula to find the observed frequency:
f' = 8000 Hz * (343 m/s + 26.67 m/s) / (343 m/s + 0 m/s) = 8668 Hz

Answer:
The frequency observed by the observer is 8668 Hz.

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