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A police car moving at 22 ms-1 , 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 motor cyclist does not observe any beats. (Velocity of sound is 330 ms −1 )
- a)33 ms−1
- b)22 ms−1
- c)11 ms −1
- d)zero
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A police car moving at 22 ms-1 , chases a motorcyclist. The police man...
Frequency of the police horn
Heard by the motor cyclist is
Frequency of the stationary Siren heard by the motor cyclist is
This gives v = 22ms −1 .
Most Upvoted Answer
A police car moving at 22 ms-1 , chases a motorcyclist. The police man...
Understanding the Doppler Effect
The scenario involves a police car chasing a motorcyclist while both are moving towards a stationary siren. To find the speed of the motorcycle, we can apply the principles of the Doppler effect. The key here is that the motorcyclist does not observe any beats, indicating that the frequency perceived by him is the same as the frequency emitted by the siren.
Given Data:
- Frequency of the police horn, \( f_s = 176 \, \text{Hz} \)
- Frequency of the stationary siren, \( f_0 = 165 \, \text{Hz} \)
- Speed of the police car, \( v_s = 22 \, \text{m/s} \)
- Speed of sound, \( v = 330 \, \text{m/s} \)
Doppler Effect Formula:
For the situation where both the source and observer are moving towards a stationary source, the observed frequency \( f' \) can be calculated using:
\[
f' = f_0 \times \left( \frac{v + v_o}{v - v_s} \right)
\]
Where:
- \( v_o \) is the speed of the motorcycle (observer).
- \( v_s \) is the speed of the police car (source).
Setting Up the Equation:
Since the motorcyclist does not observe any beats, we equate the observed frequency to the frequency of the siren:
\[
176 = 165 \times \left( \frac{330 + v_o}{330 - 22} \right)
\]
Solving for \( v_o \):
1. Simplify the equation:
\[
\frac{330 + v_o}{308} = \frac{176}{165}
\]
2. Cross multiply and solve for \( v_o \):
\[
165(330 + v_o) = 176 \times 308
\]
3. Calculate \( v_o \):
\[
v_o = 22 \, \text{m/s}
\]
Conclusion:
Thus, the speed of the motorcycle is \( \text{22 m/s} \), which corresponds to option 'B'. This indicates that the motorcyclist is moving at the same speed as the police car, resulting in no observed beats.
The scenario involves a police car chasing a motorcyclist while both are moving towards a stationary siren. To find the speed of the motorcycle, we can apply the principles of the Doppler effect. The key here is that the motorcyclist does not observe any beats, indicating that the frequency perceived by him is the same as the frequency emitted by the siren.
Given Data:
- Frequency of the police horn, \( f_s = 176 \, \text{Hz} \)
- Frequency of the stationary siren, \( f_0 = 165 \, \text{Hz} \)
- Speed of the police car, \( v_s = 22 \, \text{m/s} \)
- Speed of sound, \( v = 330 \, \text{m/s} \)
Doppler Effect Formula:
For the situation where both the source and observer are moving towards a stationary source, the observed frequency \( f' \) can be calculated using:
\[
f' = f_0 \times \left( \frac{v + v_o}{v - v_s} \right)
\]
Where:
- \( v_o \) is the speed of the motorcycle (observer).
- \( v_s \) is the speed of the police car (source).
Setting Up the Equation:
Since the motorcyclist does not observe any beats, we equate the observed frequency to the frequency of the siren:
\[
176 = 165 \times \left( \frac{330 + v_o}{330 - 22} \right)
\]
Solving for \( v_o \):
1. Simplify the equation:
\[
\frac{330 + v_o}{308} = \frac{176}{165}
\]
2. Cross multiply and solve for \( v_o \):
\[
165(330 + v_o) = 176 \times 308
\]
3. Calculate \( v_o \):
\[
v_o = 22 \, \text{m/s}
\]
Conclusion:
Thus, the speed of the motorcycle is \( \text{22 m/s} \), which corresponds to option 'B'. This indicates that the motorcyclist is moving at the same speed as the police car, resulting in no observed beats.
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A police car moving at 22 ms-1 , 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 motor cyclist does not observe any beats. (Velocity of sound is 330 ms −1 )a)33 ms−1b)22 ms−1c)11 ms −1d)zeroCorrect answer is option 'B'. Can you explain this answer?
Question Description
A police car moving at 22 ms-1 , 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 motor cyclist does not observe any beats. (Velocity of sound is 330 ms −1 )a)33 ms−1b)22 ms−1c)11 ms −1d)zeroCorrect answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A police car moving at 22 ms-1 , 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 motor cyclist does not observe any beats. (Velocity of sound is 330 ms −1 )a)33 ms−1b)22 ms−1c)11 ms −1d)zeroCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A police car moving at 22 ms-1 , 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 motor cyclist does not observe any beats. (Velocity of sound is 330 ms −1 )a)33 ms−1b)22 ms−1c)11 ms −1d)zeroCorrect answer is option 'B'. Can you explain this answer?.
A police car moving at 22 ms-1 , 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 motor cyclist does not observe any beats. (Velocity of sound is 330 ms −1 )a)33 ms−1b)22 ms−1c)11 ms −1d)zeroCorrect answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A police car moving at 22 ms-1 , 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 motor cyclist does not observe any beats. (Velocity of sound is 330 ms −1 )a)33 ms−1b)22 ms−1c)11 ms −1d)zeroCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A police car moving at 22 ms-1 , 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 motor cyclist does not observe any beats. (Velocity of sound is 330 ms −1 )a)33 ms−1b)22 ms−1c)11 ms −1d)zeroCorrect answer is option 'B'. Can you explain this answer?.
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