A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 ms-1 at an angle of 60° with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air 330 ms-1), is:

  • Option 1)

    103 Hz

  • Option 2)

    106 Hz

  • Option 3)

    97 Hz

  • Option 4)

    100 Hz

 

Answers (1)

As discussed in

frequency of sound when source is moving towards the observer and observer is moving away from source -

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

- wherein

C= Speed of sound

V_{0}= Speed of observer

V_{s}= speed of source

\nu _{0 }= Original frequency

\nu {}'= apparent frequency

 

From Doppler's effect,

\nu '= \nu _{0}\left ( \frac{v-v_{0}}{v-v_{s}} \right )

\nu '= 100 \left (\frac{v-0}{v - \left ( +9.7 \right )} \right )

\Rightarrow \nu '= \frac{100v}{v\left ( 1- \frac{9.7}{v} \right )}

            = \frac{100}{\left ( 1-\frac{9.7}{330} \right )}

\nu' = 103 Hz


Option 1)

103 Hz

This option is correct

Option 2)

106 Hz

This option is incorrect

Option 3)

97 Hz

This option is incorrect

Option 4)

100 Hz

This option is incorrect

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