question_answer

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 \[m{{s}^{-1}}\]at an angle of \[{{60}^{\text{o}}}\] 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                                                                

A)  100 Hz           

B)  103 Hz 

C)  106 Hz          

D)  97Hz

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 \[{{f}_{0}}={{f}_{s}}\left[ \frac{v}{v-{{v}_{s}}\cos {{60}^{{}^\circ }}} \right]=100\left[ \frac{330}{330-19.4\times \frac{1}{2}} \right]\] \[=100\left[ \frac{330}{300-9.7} \right]=100\left[ \frac{330}{320.3} \right]\] \[=103.02Hz\]