A train is approaching a station at 90 km/h sounding a whistle of frequency 1000 Hz. What will be the apparent frequency heard by the listener sitting on the platform if the train moves away from the station at the same speed? (speed of sound= 340 m/s)
Correct answer: A. 931.5 Hz
- A. 931.5 Hz
- B. 105.7 Hz
- C. 135.9 Hz
- D. 153.1 Hz
- E. 164.9 Hz
Explanation
To determine the apparent frequency heard by the listener, we use the Doppler effect formula:f' = f * (v + v_o) / (v + v_s)Here, f is the original frequency (1000 Hz), v is the speed of sound (340 m/s), v_o is the speed of the observer (0 m/s, as the observer is stationary), and v_s is the speed of the source (converted to 25 m/s from 90 km/h).Applying these values: f' = 1000 * (340 / (340 + 25)) = 931.5 Hz.The other options result from incorrect application of the Doppler effect formula, either due to incorrect speed conversions or misunderstanding the direction of motion, leading to incorrect frequency values.
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