JEE Advanced · 2013 · 02 Jun 2013 · Paper 2 · Waves & Sound

Two vehicles, each moving with speed

u

on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity

w

. One of these vehicles blows a whistle of frequency

f_{1}

. An observer in the other vehicle hears the frequency of the whistle to be

f_{2}

. The speed of sound in still air is

V

. The correct statement(s) is (are)

(A)If the wind blows from the observer to the source, $f_{2} > f_{1}$ .✓ Correct
(B)If the wind blows from the source to the observer, $f_{2} > f_{1}$ .✓ Correct
(C)If the wind blows from observer to the source, $f_{2} < f_{1}$ .
(D)If the wind blows from the source to the observer, $f_{2} < f_{1}$ .

Answer: (A), (B)

Solution

Using the Doppler effect formula with wind:

Wind from observer to source:

f_{2} = f_{1} [\frac{V - w + u}{V - w - u}]

Since

V - w + u > V - w - u

, we have

f_{2} > f_{1}

. ✓ (A)

Wind from source to observer:

f_{2} = f_{1} [\frac{V + w + u}{V + w - u}]

Since

V + w + u > V + w - u

, we have

f_{2} > f_{1}

. ✓ (B)

In both cases, the vehicles are approaching, so the observed frequency is higher than the source frequency regardless of wind direction.

JEE Advanced · 2013 · 02 Jun 2013 · Paper 2 · One or more correct options