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JEE Advance - Physics (2013 - Paper 2 Offline - No. 9)

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 f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is V. The correct statement(s) is(are)
If the wind blows from the observer to the source, f2 > f1.
If the wind blows from the source to the observer, f2 > f1.
If the wind blows from the observer to the source, f2 < f1
If the wind blows from the source to the observer, f2 < f1.

Explanation

Doppler's effect gives

$${f_2} = \left[ {{{v + {u_0}} \over {v - {u_s}}}} \right]{f_1}$$ ..... (1)

Let the wind speed be w and wind moves towards the source in case (i) and towards the observer in case (ii) (see figure).

JEE Advanced 2013 Paper 2 Offline Physics - Waves Question 19 English Explanation

In the case (i), u0, the speed of observer w.r.t. medium considered positive when it moves towards the source is +(u $$-$$ w) and us, the speed of source w.r.t. medium considered positive when it moves towards observer is +(u + w). Substitute these values in equation (1) to get

$${f_2} = \left[ {{{v + (u - w)} \over {v - (u + w)}}} \right]{f_1}$$,

which is greater than f1 (assuming u > w). In the case (ii), u0 is +(u + w) and us is +(u $$-$$ w). Substitute these values in equation (1) to get

$${f_2} = \left[ {{{v + (u + w)} \over {v - (u - w)}}} \right]f1$$,

which is again greater than f1.

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