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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 m/s 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 is (velocity of sound in air 330 m/s):

1. 103 Hz
2. 106 Hz
3. 97 Hz
4. 100 Hz

Correct answer: 103 Hz

Solution

The Doppler effect formula for apparent frequency is used here. Since the source is moving at an angle to the observer, only the component of velocity along the line joining the source and observer affects the frequency. The effective velocity component is 19.4 × cos(60°) = 9.7 m/s. Using the formula f' = f(v / (v - vs)), the apparent frequency is calculated as approximately 103 Hz.

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