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A police car moving at 22m/s chases a motor cyclist. The police man sounds his horn at 176Hz, while both of them move towards a stationary siren of frequency 165Hz . Calculate the speed of the motor cycle. If it is given that the motorcyclist does not observe any beats (velocity of sound =330m/s) ? Pls help me out from this problem?
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A police car moving at 22m/s chases a motor cyclist. The police man so...
To solve the problem, we will apply the principles of the Doppler effect, which describes the change in frequency of a wave in relation to an observer who is moving relative to the wave source.
Given Information:
- Speed of the police car (Vs) = 22 m/s
- Frequency of the police car's horn (fs) = 176 Hz
- Frequency of the stationary siren (f0) = 165 Hz
- Velocity of sound (v) = 330 m/s
Understanding the Situation:
- The police car is moving towards the stationary siren.
- The motorcyclist observes the sound from both the police car's horn and the siren.
Doppler Effect Formula:
For a source moving towards a stationary observer:
- Observed frequency (f') = f0 * (v / (v - Vs))
For the police car's horn:
- The observed frequency (f's) by the motorcyclist is:
f's = fs * (v / (v - Vmotorcycle))
Equating Frequencies:
Since the motorcyclist does not observe any beats, the frequency he hears from the police car's horn must equal the frequency of the siren:
- f's = f0
This leads us to:
- fs * (v / (v - Vmotorcycle)) = f0
Substituting the known values:
- 176 Hz * (330 m/s / (330 m/s - Vmotorcycle)) = 165 Hz
Solving for the Speed of the Motorcycle:
1. Rearranging gives:
330 * 176 = 165 * (330 - Vmotorcycle)
2. Expanding the equation:
58080 = 54450 - 165 * Vmotorcycle
3. Isolating Vmotorcycle yields:
Vmotorcycle = (54450 - 58080) / 165
4. Calculating gives:
Vmotorcycle = -3620 / 165 ≈ 21.95 m/s
Final Result:
- The speed of the motorcycle is approximately 21.95 m/s.
Given Information:
- Speed of the police car (Vs) = 22 m/s
- Frequency of the police car's horn (fs) = 176 Hz
- Frequency of the stationary siren (f0) = 165 Hz
- Velocity of sound (v) = 330 m/s
Understanding the Situation:
- The police car is moving towards the stationary siren.
- The motorcyclist observes the sound from both the police car's horn and the siren.
Doppler Effect Formula:
For a source moving towards a stationary observer:
- Observed frequency (f') = f0 * (v / (v - Vs))
For the police car's horn:
- The observed frequency (f's) by the motorcyclist is:
f's = fs * (v / (v - Vmotorcycle))
Equating Frequencies:
Since the motorcyclist does not observe any beats, the frequency he hears from the police car's horn must equal the frequency of the siren:
- f's = f0
This leads us to:
- fs * (v / (v - Vmotorcycle)) = f0
Substituting the known values:
- 176 Hz * (330 m/s / (330 m/s - Vmotorcycle)) = 165 Hz
Solving for the Speed of the Motorcycle:
1. Rearranging gives:
330 * 176 = 165 * (330 - Vmotorcycle)
2. Expanding the equation:
58080 = 54450 - 165 * Vmotorcycle
3. Isolating Vmotorcycle yields:
Vmotorcycle = (54450 - 58080) / 165
4. Calculating gives:
Vmotorcycle = -3620 / 165 ≈ 21.95 m/s
Final Result:
- The speed of the motorcycle is approximately 21.95 m/s.
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A police car moving at 22m/s chases a motor cyclist. The police man sounds his horn at 176Hz, while both of them move towards a stationary siren of frequency 165Hz . Calculate the speed of the motor cycle. If it is given that the motorcyclist does not observe any beats (velocity of sound =330m/s) ? Pls help me out from this problem?
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A police car moving at 22m/s chases a motor cyclist. The police man sounds his horn at 176Hz, while both of them move towards a stationary siren of frequency 165Hz . Calculate the speed of the motor cycle. If it is given that the motorcyclist does not observe any beats (velocity of sound =330m/s) ? Pls help me out from this problem? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A police car moving at 22m/s chases a motor cyclist. The police man sounds his horn at 176Hz, while both of them move towards a stationary siren of frequency 165Hz . Calculate the speed of the motor cycle. If it is given that the motorcyclist does not observe any beats (velocity of sound =330m/s) ? Pls help me out from this problem? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A police car moving at 22m/s chases a motor cyclist. The police man sounds his horn at 176Hz, while both of them move towards a stationary siren of frequency 165Hz . Calculate the speed of the motor cycle. If it is given that the motorcyclist does not observe any beats (velocity of sound =330m/s) ? Pls help me out from this problem?.
A police car moving at 22m/s chases a motor cyclist. The police man sounds his horn at 176Hz, while both of them move towards a stationary siren of frequency 165Hz . Calculate the speed of the motor cycle. If it is given that the motorcyclist does not observe any beats (velocity of sound =330m/s) ? Pls help me out from this problem? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A police car moving at 22m/s chases a motor cyclist. The police man sounds his horn at 176Hz, while both of them move towards a stationary siren of frequency 165Hz . Calculate the speed of the motor cycle. If it is given that the motorcyclist does not observe any beats (velocity of sound =330m/s) ? Pls help me out from this problem? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A police car moving at 22m/s chases a motor cyclist. The police man sounds his horn at 176Hz, while both of them move towards a stationary siren of frequency 165Hz . Calculate the speed of the motor cycle. If it is given that the motorcyclist does not observe any beats (velocity of sound =330m/s) ? Pls help me out from this problem?.
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A police car moving at 22m/s chases a motor cyclist. The police man sounds his horn at 176Hz, while both of them move towards a stationary siren of frequency 165Hz . Calculate the speed of the motor cycle. If it is given that the motorcyclist does not observe any beats (velocity of sound =330m/s) ? Pls help me out from this problem?, a detailed solution for A police car moving at 22m/s chases a motor cyclist. The police man sounds his horn at 176Hz, while both of them move towards a stationary siren of frequency 165Hz . Calculate the speed of the motor cycle. If it is given that the motorcyclist does not observe any beats (velocity of sound =330m/s) ? Pls help me out from this problem? has been provided alongside types of A police car moving at 22m/s chases a motor cyclist. The police man sounds his horn at 176Hz, while both of them move towards a stationary siren of frequency 165Hz . Calculate the speed of the motor cycle. If it is given that the motorcyclist does not observe any beats (velocity of sound =330m/s) ? Pls help me out from this problem? theory, EduRev gives you an
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