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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 $60^\circ$ 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:
A
97 Hz
B
100 Hz
C
103 Hz
D
106 Hz
Detailed Solution
Component of source velocity towards the observer: $v_s\cos 60^\circ = \frac{19.4}{2} = 9.7$ m/s
$f_0 = f_s\left(\frac{v}{v - v_s\cos60^\circ}\right) = 100\left(\frac{330}{330 - 9.7}\right) \approx 103$ Hz
$f_0 = f_s\left(\frac{v}{v - v_s\cos60^\circ}\right) = 100\left(\frac{330}{330 - 9.7}\right) \approx 103$ Hz