A source of sound emits sound waves at frequency f_{0}. It is moving towards an observer with fixed speed v_{s}(v_{s}< v,where\: v \: is \: the \: speed\: of \: sound \: in\: air) If the observer were to move towards the source with speed v_{0}, one of the following two graphs (A and B) will give the correct variation of the frequency f heard by the observer as v_{0} is changed.

The variation of f with v_{o} is given correctly by :

 

  • Option 1)

    graph A with slope  =   \frac{f_{0}}{\left ( \nu -\nu _{s} \right )}

  • Option 2)

    graph A with slope  =     \frac{f_{0}}{\left ( \nu +\nu _{s} \right )}

  • Option 3)

    graph B with slope  =    \frac{f_{0}}{\left ( \nu -\nu _{s} \right )}

  • Option 4)

      graph B with slope  =     \frac{f_{0}}{\left ( \nu +\nu _{s} \right )}

 

Answers (1)

As we learnt in

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

\nu {}'= \nu _{0}.\frac{C}{C-V_{\Delta }}
 

- wherein

C= speed of sound

V_{\Delta }= speed of source

\nu _{0}= original frequency

\nu {}'= apparent frequency

 

 Graph A with slope =\frac{f_{0}}{(\upsilon-\upsilon_{s})}

Correct option is 1.

 


Option 1)

graph A with slope  =   \frac{f_{0}}{\left ( \nu -\nu _{s} \right )}

This is the correct option.

Option 2)

graph A with slope  =     \frac{f_{0}}{\left ( \nu +\nu _{s} \right )}

This is an incorrect option.

Option 3)

graph B with slope  =    \frac{f_{0}}{\left ( \nu -\nu _{s} \right )}

This is an incorrect option.

Option 4)

  graph B with slope  =     \frac{f_{0}}{\left ( \nu +\nu _{s} \right )}

This is an incorrect option.

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