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An observer is standing 500 m away from a vertical hill. Starting between the observer and the hill, a police van sounding a siren of frequency 1000 Hz moves towards the hill with a uniform speed. If the frequency of the sound heard directly from the siren is 970 Hz, the frequency of the sound heard after reflection from the hill (in Hz) is about, (velocity of sound=330 ms^-1)

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1042

1012

1022

1032

answer is B.

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Detailed Solution

$970 = 1000 (\frac{v}{v + v_{s}}) \Rightarrow v_{s} = \frac{3 v}{97}$
Echo frequency: $n^{1} = n [\frac{v}{v - v_{s}}]$
$= n [\frac{v}{v - \frac{3 v}{97}}] = 1000 \times \frac{97}{94} = 1032 Hz$

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