When a car is approaching the observer, the frequency of horn is 100 Hz. After passing the observer, it is 50 Hz. If the observer moves with the car, the frequency will be x/3 Hz where x = ________________. Numerical answer type. Work it out, then open the answer.

Answer: 200. 100 = f (v)/(v - u) and 50 = f (v)/(v + u), so (v + u)/(v - u) = 2 ⇒ u = v/3. Actual frequency f = 100 (v - u)/(v) = 100 × 2/3 = 200/3 Hz. Moving with the car there is no relative motion, so the observer hears 200/3 Hz. x = 200

When a car is approaching the observer, the frequency of horn is 100… | JEE Main 2022 (26 Jul, Shift 1)

Q40JEE Main 2022 · 26 JUL · SHIFT 1Medium

Doppler Effect

When a car is approaching the observer, the frequency of horn is $100\text{ Hz}$ . After passing the observer, it is $50\text{ Hz}$ . If the observer moves with the car, the frequency will be $\frac{x}{3}\text{ Hz}$ where $x =$ ________________.

Numerical answer type. Work it out, then open the answer.

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Answer: 200

$100 = f\,\dfrac{v}{v - u}$ and $50 = f\,\dfrac{v}{v + u}$ , so $\dfrac{v + u}{v - u} = 2 \Rightarrow u = \dfrac{v}{3}$ .
Actual frequency $f = 100\,\dfrac{v - u}{v} = 100 \times \dfrac{2}{3} = \dfrac{200}{3}\text{ Hz}$ .
Moving with the car there is no relative motion, so the observer hears $\dfrac{200}{3}\text{ Hz}$ .
$x = 200$

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