A car P travelling at 20 ms⁻¹ sounds its horn at a frequency of 400 Hz. Another car Q is travelling behind the first car in the same direction with a velocity 40 ms⁻¹. The frequency heard by the passenger of the car Q is approximately [Take, velocity of sound = 360 ms⁻¹ ] (a) 485 Hz (b) 514 Hz (c) 421 Hz (d) 471 Hz

Answer: (c). Q40 m/sP20 m/ssound P to Q Sound travels backward from P to Q. Q moves towards P (towards the sound): numerator v + 40. P moves away from Q: denominator v + 20. n' = 400 × (360 + 40)/(360 + 20) = 400 × (400)/(380) n' ≈ 421 Hz. So the answer is (c) 421 Hz.

A car P travelling at 20 ms⁻¹ sounds its horn at a frequency of 400… | JEE Main 2023 (11 Apr, Shift 2)

Q32JEE Main 2023 · 11 APR · SHIFT 2Easy

Doppler Effect

A car P travelling at $20\text{ ms}^{-1}$ sounds its horn at a frequency of $400\text{ Hz}$ . Another car $Q$ is travelling behind the first car in the same direction with a velocity $40\text{ ms}^{-1}$ . The frequency heard by the passenger of the car $Q$ is approximately [Take, velocity of sound $= 360\text{ ms}^{-1}$ ]

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Answer: (c)

Sound travels backward from P to Q. Q moves towards P (towards the sound): numerator $v + 40$ .
P moves away from Q: denominator $v + 20$ .
$n' = 400 \times \frac{360 + 40}{360 + 20} = 400 \times \frac{400}{380}$
$n' \approx 421$ Hz. So the answer is (c) 421 Hz.

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