A car P travelling at 20m s ^ - 1 sounds its horn at a frequency of...

A car

P

travelling at

20m{s}^{- 1}

sounds its horn at a frequency of

400Hz

. Another car

Q

is travelling behind the first car in the same direction with a velocity

40m{s}^{- 1}

. The frequency heard by the passenger of the car

Q

is approximately [Take, velocity of sound

= 360m{s}^{- 1}

]

A car P travelling at 20m s ^ - 1 sounds its horn at a frequency of 400Hz . Another car Q is travelling behind the

Options

A $421Hz$
B $471Hz$
C $485Hz$
D $514Hz$

Correct answer

B. $471Hz$

Step-by-step solution

A car P travelling at 20m s ^ - 1 sounds its horn at a frequency of 400Hz . Another car Q is travelling behind the

Let velocity of sound in air be $vm{s}^{- 1}$ . Using Doppler formula,

$f = {f}_{0}\left(\dfrac{v + {v}_{o}}{v - {v}_{s}}\right) = {f}_{0}\left(\dfrac{v + 40}{v - 20}\right)$
$= 400\left(\dfrac{360 + 40}{340}\right)$
$\approx 471Hz$

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