Wave Motion 4 Question 11
11. A police car moving at $22 m / s$ chases a motorcyclist. The police man 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 $=330 m / s$ ).
(2003, 2M)
(a) $33 m / s$
(b) $22 m / s$
(c) Zero
(d) $11 m / s$
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Answer:
Correct Answer: 11. (b)
Solution:
- The motorcyclist observes no beats. So, the apparent frequency observed by him from the two sources must be equal.
$$ \begin{aligned} f _1 & =f _2 \\ \therefore \quad 176\left(\frac{330-v}{330-22}\right) & =165\left(\frac{330+v}{330}\right) \end{aligned} $$
Solving this equation, we get $v=22 m / s$
