question_answer

A source of sound S emitting waves of frequency 100 Hz and an observer 0 are located at some distance from each other. The source is moving with a speed of \[19.4m{{s}^{-1}}\] at an angle of \[60{}^\circ \] with the source observer line as shown in the figure. .The observer is at rest. The apparent frequency observed by the observer is (velocity of sound in air \[330m{{s}^{-1}}\])

A)  103 Hz         

B)         106 Hz

C) 97 Hz               

D) 100 Hz

Correct Answer: A

Solution :

[a] Here, original frequency of sound, \[{{f}_{0}}=100\,Hz\] Speed of source \[{{V}_{s}}=19.4\,\cos \,60{}^\circ =9.7\] From Doppler?s formula \[f={{f}_{0}}\left( \frac{V-{{V}_{0}}}{V-{{V}_{s}}} \right)\] \[f=100\left( \frac{V-0}{V-(+9.7)} \right)\] \[f=100\frac{V}{V\left( 1-\frac{9.7}{V} \right)}=\frac{100}{\left( 1-\frac{9.7}{330} \right)}=103\,Hz\] Apparent frequency \[f=103\,Hz\]