question_answer

A source +e 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 \[19.4\,m{{s}^{-1}}\] at an angle of \[{{60}^{o}}\] 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 \[330\,m{{s}^{-1}}\]), is                                                                                                  [NEET (Re) 2015]

A)  100 Hz       

B) 103 Hz

C)       106 Hz   

D)  97 Hz

Correct Answer: B

Solution :

Given, as a source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance. Such that, source is moving with a speed of 19.4 m/s at angle \[60{}^\circ \] with source-observer line as shown in figure.

The apparent frequency heard by observer

\[{{f}_{0}}={{f}_{s}}\left[ \frac{v}{v-{{v}_{s}}\cos {{60}^{{}^\circ }}} \right]=100\left[ \frac{330}{330-19.4\times \frac{1}{2}} \right]\]

\[=100\left[ \frac{330}{300-9.7} \right]=100\left[ \frac{330}{320.3} \right]\]

\[=103.02Hz\]