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BITSAT 2018
Exam
BITSAT
Year
2018
Subject
Physics
Chapter
Waves and Sound

BITSAT 2018 · Physics · Waves and Sound

A train moves towards a stationary observer with speed 34ms^ - 1 ....

A train moves towards a stationary observer with speed 34ms−134ms^{- 1}. The train blows whistle and its frequency is registered by the observer as ν1{ν}_{1}. If the train's speed is reduced to 17ms−1,17ms^{- 1}, then the frequency registered is ν2{ν}_{2}. If the speed of sound is 340ms−1340ms^{- 1}, then the ratio ν1ν2\dfrac{ν1}{ν2} is

Options

  1. A1918\dfrac{19}{18}
  2. B1819\dfrac{18}{19}
  3. C22
  4. D1/21 / 2

Correct answer

A. 1918\dfrac{19}{18}

Step-by-step solution

According to Doppler's effect, the approximate frequency heard by the stationary observer,

ν=CC−vsν0ν = \dfrac{C}{C - {v}_{s}}{ν}_{0}

Case (I) vs=34ms−1{v}_{s} = 34ms^{- 1}, where& C=C =Speed of sound in air,

vs={v}_{s} = Speed of source, and& ν0={ν}_{0} = frequency of the source.

∴ {ν}_{1} = \left(\dfrac{340}{340 - 34}\right){ν}_{0}</p><p>=\dfrac{340}{306} {ν}_{0} . . . . \left( i\right)</p><p>Case(ii)</p><p>Case (ii){v}_{s} = 17ms^{- 1}<br/><br />∴ {ν}_{2} = 340340−17ν0=340323ν0....(ii)</p><p>FromEq.(i)\dfrac{340}{340 - 17} {ν}_{0} = \dfrac{340}{323} {ν}_{0} . . . .\left(ii\right)</p><p>From Eq. (i) and (ii), we get

∴ ν1ν2=340/306340/323=323306=1918\dfrac{ν1}{ν2} = \dfrac{340 / 306}{340 / 323} = \dfrac{323}{306} = \dfrac{19}{18}

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