A source of sound emitting 1200 Hz note travels along a straight line at a speed of $170 m s^{- 1}$ . A detector is placed at a distance 200 m from the line of motion of the source. The frequency of the sound received by the detector when it is closest is (velocity of sound is $340 m s^{- 1}$

1600 Hz

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800 Hz

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2400 Hz

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none of these

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Solution

The correct option is A 1600 Hz
$f_{1} \frac{v}{v + v_{s}} f = \frac{340}{510} \times 1200 = 800 H z;$
$f_{2} = \frac{v}{v - v_{s}} f = \frac{340}{170} \times = 2400 H z$
$f = \frac{f_{1} + f_{2}}{2} = \frac{800 + 2400}{2} = 1600 H z .$

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