A submarine (A) travelling at 18 km/hr is being chased along the line… | JEE Main 2019 (12 Apr, Shift 1)

Q57JEE Main 2019 · 12 APR · SHIFT 1Medium

Doppler Effect

A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine (B) travelling at 27 km/hr. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency $v$ . The value of $v$ is close to: (Speed of sound in water =1500 ms–1)

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Answer: (b)

$v_B = 27\text{ km/h} = 7.5\text{ m/s}$ (chasing), $v_A = 18\text{ km/h} = 5\text{ m/s}$ (ahead, same direction).
A receives: $f_1 = 500\,\dfrac{1500 - 5}{1500 - 7.5} = 500\,\dfrac{1495}{1492.5}$ (A moves away, B moves towards).
B receives the echo: $f_2 = f_1\,\dfrac{1500 + 7.5}{1500 + 5} = f_1\,\dfrac{1507.5}{1505}$
$f_2 \approx 500 \times 1.00334 \approx 501.7\text{ Hz}$
So the answer is (b) 502 Hz.

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Doppler Effect question from JEE Main 2019 (12 Apr, Shift 1)

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