A police man is standing. A bullet just crosses his ear with $175 m / s$ . If the frequency is $800 H z$ . Find the frequency heard by the policeman $v_{s} = 350 m / s$ :

1067 H z

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1600 H z

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533 H z

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none of the above

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Solution

The correct option is A $1067 H z$
Here bullet will work as a source and police man will work as a object
$v_{s o u r c e} = v_{b u l l e t} = 175 m / s$ $v_{o b j e c t} = v_{p o l i c e} = 0 m / s$
case(i) while approaching
frequency heard by policeman $= f_{o} \times \frac{v_{s} + v_{p}}{v_{s} - v_{b}}$
$f_{1} = 800 \times \frac{350}{350 - 175}$

$= 800 \frac{350}{175} = 1600 H z$
case(ii)while receding
$f_{2} = f_{o} \times \frac{v_{s} + v_{p}}{v_{s} + v_{b}}$

$= f \frac{v_{s}}{v_{s} + v_{b}}$

$= 800 \frac{350}{525} = \frac{1600}{3}$

$f = \frac{f_{1} + f_{2}}{2} = \frac{1600 + \frac{1600}{3}}{2}$

$= \frac{3200}{3} = 1067 H z$

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A police man is standing. A bullet just crosses his ear with 175 m/s. If the frequency is 800 Hz. Find the frequency heard by the policeman vs=350 m/s :

A police man is standing. A bullet just crosses his ear with $175 m / s$ . If the frequency is $800 H z$ . Find the frequency heard by the policeman $v_{s} = 350 m / s$ :