First slide

Doppler

Question

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

Moderate

A

106 Hz
B

97 Hz
C

100 Hz
D

103 Hz

Solution

Here,
$Frequency of source, v_{0} = 100 Hz$
$Velocity of source, v_{s} = 19.4 {ms}^{- 1}$
$Velocity of sound in air, v = 330 {ms}^{- 1}$
As the velocity of source along the source observer line is $v_{s}$ cos 60° and the observer is at rest, so the apparent frequency observed by the observer is
$v = v_{0} (\frac{v}{v - v_{s} \cos 60 °})$
$= (100 Hz) (\frac{330 {ms}^{- 1}}{330 {ms}^{- 1} - (19.4 {ms}^{- 1}) (\frac{1}{2})})$
$= (100 Hz) (\frac{330 {ms}^{- 1}}{330 {ms}^{- 1} - 9.7 {ms}^{- 1}})$
$= (100 Hz) (\frac{330 {ms}^{- 1}}{320.3 {ms}^{- 1}}) = 103 Hz$

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