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A car is travelling at $\frac{v}{10} m s^{- 1}$ and sounds horn of frequency 990 Hz. The apparent frequency heard by a police chasing the car at $\frac{v}{9} m s^{- 1}$ where V is velocity of sound

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900 Hz

990 Hz

1000 Hz

answer is C.

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Detailed Solution

By doppler's effect

$f^{'} = (\frac{v + v_{o}}{v + v_{S}}) \Rightarrow f^{'} = 990 (\frac{v + \frac{v}{9}}{v + \frac{v}{10}})$

$f^{'} = 990 (\frac{10 V}{9} \times \frac{10}{11 V}) = (\frac{100}{99}) 990 = 1000 Hz$

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