A police car moving at 22 m/s 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 :
Correct answer: B. 22 m/s
- A. 33 m/s
- B. 22 m/s
- C. Zero
- D. 11 m/s
Explanation
To solve this problem, we apply the concept of the Doppler effect. The condition for no beats is when the frequencies from the police car's horn and the siren match as perceived by the motorcyclist. Since no beats are heard, the motorcyclist must perceive the same frequency from both the horn and the siren. The police car is moving towards the stationary siren, but the motorcyclist hears no beats, indicating that the motorcyclist must be moving at the same speed as the police car (22 m/s) to maintain the same relative motion with both sound sources. Thus, the correct answer is 22 m/s.Other options are incorrect because they would result in a frequency difference between the sounds from the police car and the siren, leading to the perception of beats.
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