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Doppler Effect question from JEE Main 2015

Q67JEE Main 2015Difficult

Doppler Effect

A train is moving on a straight track with speed $20\text{ ms}^{-1}.$ It is blowing its whistle at the frequency of $1000\text{ Hz}$ . The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound $= 320\text{ ms}^{-1}$ ) close to:

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Answer: (d)

Approaching: $f_1 = 1000 \times \frac{320}{320 - 20} \approx 1066.7$ Hz
Receding: $f_2 = 1000 \times \frac{320}{320 + 20} \approx 941.2$ Hz
Percentage change $= \frac{f_1 - f_2}{f_1} \times 100 = \frac{125.5}{1066.7} \times 100 \approx 12\%$
So the answer is (d) $12\%$ .

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