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° 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) 106 Hz (b) 97 Hz (c) 100 Hz (d) 103 Hz

Answer: (d). Only the velocity component along the source–observer line matters: u = 19.4cos 60° = 9.7 m/s towards O. f' = f (v)/(v - u) = 100 × (330)/(330 - 9.7) = (33000)/(320.3) f' ≈ 103 Hz So the answer is (d) 103 Hz.

A source of sound S emitting waves of frequency 100 Hz and an… | NEET 2015 (AIPMT)

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Doppler Effect

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° 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

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Answer: (d)

Only the velocity component along the source–observer line matters: $u = 19.4\cos 60^\circ = 9.7\text{ m/s}$ towards O.
$f' = f\,\dfrac{v}{v - u} = 100 \times \dfrac{330}{330 - 9.7} = \dfrac{33000}{320.3}$
$f' \approx 103\text{ Hz}$
So the answer is (d) 103 Hz.

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