JEE Main · 2015 · 04 Apr 2015 · Offline · Waves & Sound

A train is moving on a straight track with speed

20 ms^{- 1}

. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound

= 320 ms^{- 1}

) close to :

(A) $12%$ ✓ Correct
(B) $18%$
(C) $24%$
(D) $6%$

Answer: (A)

Solution

As the whistle rushes towards the listener its pitch is raised to

f_{1} = f_{0} \frac{v}{v - v _{s}} = 1000 \times \frac{320}{300}

, and the instant it has passed and is receding the pitch drops to

f_{2} = f_{0} \frac{v}{v + v _{s}} = 1000 \times \frac{320}{340}

. The whole jump the person hears, taken as a fraction of the approaching frequency, is

\frac{f _{1} - f _{2}}{f _{1}} = 1 - \frac{300}{340} = \frac{40}{340}

, which is close to

12%

JEE Main · 2015 · 04 Apr 2015 · Offline · Single correct option

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JEE Main · 2015 · 04 Apr 2015 · Offline · Waves & Sound

Solution

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