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A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is f_{1}. If the speed of the train is reduced to 17 m/s, the frequency registered is f_{2}. If the speed of sound is 340 m/s, then the ratio f_{1}/f_{2} is : 

  • Option 1)

  • Option 2)

  • Option 3)

     

  • Option 4)

Answers (1)

best_answer

 

Frequency of sound when observer is stationary and source is moving towards observer -

\nu {}'= \nu _{0}.\frac{C}{C-V_{s}}
 

- wherein

C= speed of sound

V_{s}= speed of source

\nu _{0}= original frequency

\nu {}'= apparent frequency

v_{0}=0\: \: \: \: \: v_{s}.Train

                    \leftarrow

\dot{0}                 \dot{s}

                   

 

f_{1}=f_{0}\left ( \frac{V_{0}}{V_{0}-V_{S}} \right )\\\\(I)\rightarrow f_{1}=f_{0}\left ( \frac{340}{340-34} \right )-----(1)\\\\\\(II)\rightarrow now\: \: V_{s}=17m/s\\\\: so\: \: f_{2}=f_{0}\left ( \frac{V_{0}}{V_{0}-V_{s}} \right )\\\\f_{2}=f_{0}\left ( \frac{340}{340-17} \right )---(2)

 

from (1) and (2)

\frac{f_{1}}{f_{2}}=\frac{340-17}{340-34}=\frac{323}{306}\\\\\Rightarrow \frac{f_{1}}{f_{2}}=\frac{19}{18}

 


Option 1)

Option 2)

Option 3)

 

Option 4)

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