A police car moving at 22 m s- 1 chases a motorcyclist. The policeman sounds his horn at 176 Hz , while both of them move towards a stationary siren of frequency 165 Hz . Calculate the speed of the motorcycle if it is given that the motorcyclist does not observe any beats (speed of sound = 330 m s- 1 )

Question

A police car moving at 22 m s- 1 chases a motorcyclist. The policeman sounds his horn at 176 Hz , while both of them move towards a stationary siren of frequency 165 Hz . Calculate the speed of the motorcycle if it is given that the motorcyclist does not observe any beats (speed of sound = 330 m s- 1 ) <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-oxrcso1twna7hiuf.jpg" /> (A) 33ms- 1 (B) 22ms- 1 (C) Zero (D) 11ms- 1

Tardigrade Admin · Accepted Answer

The motorcyclist observes no beats. So the apparent frequency observed by him from the two sources must be equal.

f_{1} = f_{2}

∴ 176 (\frac{330 - v}{330 - 22}) = 165 (\frac{330 + v}{330})

Solving this equation, we get

v = 22 m s^{- 1}

$33 m s^{- 1}$

$22 m s^{- 1}$

Zero

$11 m s^{- 1}$

The motorcyclist observes no beats. So the apparent frequency observed by him from the two sources must be equal.
$f_{1} = f_{2}$
$∴ 176 (\frac{330 - v}{330 - 22}) = 165 (\frac{330 + v}{330})$
Solving this equation, we get $v = 22 m s^{- 1}$

33ms−1

22ms−1

Zero

11ms−1

The motorcyclist observes no beats. So the apparent frequency observed by him from the two sources must be equal. f1​=f⁡2​ ∴176(330−22330−v​)=165(330330+v⁡​) Solving this equation, we get v=22 m s−1

$33 m s^{- 1}$

$22 m s^{- 1}$

$11 m s^{- 1}$

The motorcyclist observes no beats. So the apparent frequency observed by him from the two sources must be equal.
$f_{1} = f_{2}$
$∴ 176 (\frac{330 - v}{330 - 22}) = 165 (\frac{330 + v}{330})$
Solving this equation, we get $v = 22 m s^{- 1}$