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 = $330 \, m \, s^{- 1}$ )

• A. $33ms^{- 1}$
• B. $22ms^{- 1}$
• C. Zero
• D. $11ms^{- 1}$

Answer 1

Answer: (B)

The motorcyclist observes no beats. So the apparent frequency observed by him from the two sources must be equal.
$ f _{1} = f ⁡_{2}$
$\therefore 1 7 6 \left(\frac{3 3 0 - v }{3 3 0 - 2 2}\right) = 1 6 5 \left(\frac{3 3 0 + v ⁡}{3 3 0}\right)$
Solving this equation, we get $v =22\text{ m s}^{- 1}$