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Question
A traffic policeman standing on a road sounds a whistle emitting the main frequency of 2.00 kHz. What could be the apparent frequency heard by a scooter-driver approaching the policeman at a speed of 36.0 km h−1? Speed of sound in air = 340 m s−1.
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Solution
Velocity of sound in air v = 340 ms−1
Velocity of scooter-driver \[v_o\]= 36 kmh−1 =
\[36 \times \frac{5}{18} = 10 {\text { ms }}^{- 1}\]
Frequency of sound of whistle \[f_o\]= 2 kHz
Apparent frequency \[\left( f \right)\] heard by the scooter-driver approaching the policeman is given by :
\[f = \left( \frac{v + v_o}{v} \right) \times f_o\]
\[f = \left( \frac{340 + 10}{340} \right) \times 2\]
\[ = \frac{350 \times 2}{340} \text { kHz }\]
\[ = 2 . 06 \text{ kHz }\]
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