A sound source S is moving along a straight track with speed v, and… | JEE Main 2020 (6 Sep, Shift 1)

Q50JEE Main 2020 · 6 SEP · SHIFT 1Difficult

Doppler Effect

A sound source S is moving along a straight track with speed v, and is emitting, sound of frequency v0 (see figure). An observer is standing at a finite distance, at the point O, from the track. The time variation of frequency heard by the observer is best represented by:

(t0 represents the instant when the distance between the source and observer is minimum)

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Answer: (d)

Heard frequency $\nu = \frac{\nu_0 v_{sound}}{v_{sound} - v\cos\theta}$ , where $\theta$ is the angle between the source velocity and the line to O.
Far before O: $\theta \approx 0$ , so $\nu$ is maximum and nearly constant, above $\nu_0$ .
As the source passes, $\cos\theta$ falls smoothly from $+1$ to $-1$ , so $\nu$ decreases continuously, through about $\nu_0$ near $t_0$ .
Far after O: $\nu$ levels off at a minimum below $\nu_0$ .
So the answer is (d), the smooth decreasing curve.

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Doppler Effect question from JEE Main 2020 (6 Sep, Shift 1)

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