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An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P2 open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 is
- a)8/3
- b)3/8
- c)1/6
- d)1/3
Correct answer is option 'C'. Can you explain this answer?
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Explanation:
To understand why the ratio of the length of pipe P1 to that of pipe P2 is 1/6, we need to analyze the resonant frequencies of these two pipes and the given tuning fork.
Resonant Frequencies:
The resonant frequency of an organ pipe closed at one end is given by:
f1 = v / 4L1
Where:
- f1 is the frequency of the first harmonic (fundamental frequency) of pipe P1,
- v is the speed of sound in air (assumed to be constant),
- L1 is the length of pipe P1.
Similarly, the resonant frequency of an organ pipe open at both ends is given by:
f2 = v / 2L2
Where:
- f2 is the frequency of the third harmonic of pipe P2,
- L2 is the length of pipe P2.
Resonance Condition:
For resonance to occur, the frequency of the tuning fork must match the resonant frequency of the pipe. In this case, the tuning fork is in resonance with both pipe P1 and pipe P2.
Therefore, we can write the resonance condition for pipe P1 as:
f1 = f_tuning_fork
And the resonance condition for pipe P2 as:
f2 = f_tuning_fork
Given Information:
From the given information, we know that pipe P1 is vibrating in its first harmonic (fundamental frequency) and pipe P2 is vibrating in its third harmonic.
Therefore, we can write the following relationship between the frequencies:
f2 = 3f1
Deriving the Ratio:
Using the resonance conditions and the relationship between frequencies, we can equate the two equations:
v / 2L2 = 3(v / 4L1)
Simplifying the equation:
2L1 = 3L2
Dividing both sides by L2:
2L1 / L2 = 3
Therefore, the ratio of the length of pipe P1 to that of pipe P2 is 2/3.
However, we need to find the ratio of L1 to L2. Since L1 is the length of pipe P1 and L2 is the length of pipe P2, the ratio is:
L1 / L2 = 1 / 3
Therefore, the correct answer is option C: 1/6.
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An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P2 open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 isa)8/3b)3/8c)1/6d)1/3Correct answer is option 'C'. Can you explain this answer?
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An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P2 open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 isa)8/3b)3/8c)1/6d)1/3Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P2 open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 isa)8/3b)3/8c)1/6d)1/3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P2 open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 isa)8/3b)3/8c)1/6d)1/3Correct answer is option 'C'. Can you explain this answer?.
An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P2 open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 isa)8/3b)3/8c)1/6d)1/3Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P2 open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 isa)8/3b)3/8c)1/6d)1/3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P2 open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 isa)8/3b)3/8c)1/6d)1/3Correct answer is option 'C'. Can you explain this answer?.
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