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An organ pipe P1 closed at one end vibrating in its first overtone and another pipe P2 open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1 and P2 is
- a)1 : 2
- b)1 : 3
- c)3 : 8
- d)3 : 4
Correct 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 overtone and...
Given:
- Organ pipe P1 closed at one end vibrating in its first overtone
- Pipe P2 open at both ends vibrating in its third overtone
- Pipes P1 and P2 are in resonance with a given tuning fork
To find: Ratio of lengths of P1 and P2
Solution:
- When an organ pipe is in resonance with a tuning fork, the frequency of the sound wave produced by the pipe is equal to the frequency of the tuning fork.
- For an organ pipe closed at one end, the frequency of the sound wave produced in the first overtone is three times the fundamental frequency. Hence, if f is the frequency of the tuning fork, the frequency of the sound wave produced by P1 is 3f.
- For an organ pipe open at both ends, the frequency of the sound wave produced in the third overtone is three times the fundamental frequency. Hence, if f is the frequency of the tuning fork, the frequency of the sound wave produced by P2 is 9f.
- Since P1 and P2 are in resonance with the same tuning fork, their frequencies are equal: 3f = 9f/3, which simplifies to f = 3f/9. Hence, the fundamental frequency of the tuning fork is f = 27/9 = 3 Hz.
- Let L1 and L2 be the lengths of P1 and P2, respectively.
- For a pipe closed at one end, the wavelength of the sound wave produced in the first overtone is four times the length of the pipe. Hence, the wavelength of the sound wave produced by P1 is 4L1.
- For a pipe open at both ends, the wavelength of the sound wave produced in the third overtone is twice the length of the pipe. Hence, the wavelength of the sound wave produced by P2 is 2L2/3.
- Since the frequency of the sound wave produced by P1 is equal to the frequency of the sound wave produced by P2, their wavelengths are also equal: 4L1 = 2L2/3, which simplifies to L1/L2 = 3/8.
Therefore, the ratio of lengths of P1 and P2 is 3 : 8. Hence, option (c) is the correct answer.
- Organ pipe P1 closed at one end vibrating in its first overtone
- Pipe P2 open at both ends vibrating in its third overtone
- Pipes P1 and P2 are in resonance with a given tuning fork
To find: Ratio of lengths of P1 and P2
Solution:
- When an organ pipe is in resonance with a tuning fork, the frequency of the sound wave produced by the pipe is equal to the frequency of the tuning fork.
- For an organ pipe closed at one end, the frequency of the sound wave produced in the first overtone is three times the fundamental frequency. Hence, if f is the frequency of the tuning fork, the frequency of the sound wave produced by P1 is 3f.
- For an organ pipe open at both ends, the frequency of the sound wave produced in the third overtone is three times the fundamental frequency. Hence, if f is the frequency of the tuning fork, the frequency of the sound wave produced by P2 is 9f.
- Since P1 and P2 are in resonance with the same tuning fork, their frequencies are equal: 3f = 9f/3, which simplifies to f = 3f/9. Hence, the fundamental frequency of the tuning fork is f = 27/9 = 3 Hz.
- Let L1 and L2 be the lengths of P1 and P2, respectively.
- For a pipe closed at one end, the wavelength of the sound wave produced in the first overtone is four times the length of the pipe. Hence, the wavelength of the sound wave produced by P1 is 4L1.
- For a pipe open at both ends, the wavelength of the sound wave produced in the third overtone is twice the length of the pipe. Hence, the wavelength of the sound wave produced by P2 is 2L2/3.
- Since the frequency of the sound wave produced by P1 is equal to the frequency of the sound wave produced by P2, their wavelengths are also equal: 4L1 = 2L2/3, which simplifies to L1/L2 = 3/8.
Therefore, the ratio of lengths of P1 and P2 is 3 : 8. Hence, option (c) is the correct answer.
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An organ pipe P1 closed at one end vibrating in its first overtone and...
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An organ pipe P1 closed at one end vibrating in its first overtone and another pipe P2 open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1 and P2 isa)1 : 2b)1 : 3c)3 : 8d)3 : 4Correct 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 overtone and another pipe P2 open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1 and P2 isa)1 : 2b)1 : 3c)3 : 8d)3 : 4Correct 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 overtone and another pipe P2 open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1 and P2 isa)1 : 2b)1 : 3c)3 : 8d)3 : 4Correct 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 overtone and another pipe P2 open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1 and P2 isa)1 : 2b)1 : 3c)3 : 8d)3 : 4Correct answer is option 'C'. Can you explain this answer?.
An organ pipe P1 closed at one end vibrating in its first overtone and another pipe P2 open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1 and P2 isa)1 : 2b)1 : 3c)3 : 8d)3 : 4Correct 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 overtone and another pipe P2 open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1 and P2 isa)1 : 2b)1 : 3c)3 : 8d)3 : 4Correct 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 overtone and another pipe P2 open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1 and P2 isa)1 : 2b)1 : 3c)3 : 8d)3 : 4Correct answer is option 'C'. Can you explain this answer?.
Solutions for An organ pipe P1 closed at one end vibrating in its first overtone and another pipe P2 open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1 and P2 isa)1 : 2b)1 : 3c)3 : 8d)3 : 4Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
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An organ pipe P1 closed at one end vibrating in its first overtone and another pipe P2 open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1 and P2 isa)1 : 2b)1 : 3c)3 : 8d)3 : 4Correct answer is option 'C'. Can you explain this answer?, a detailed solution for An organ pipe P1 closed at one end vibrating in its first overtone and another pipe P2 open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1 and P2 isa)1 : 2b)1 : 3c)3 : 8d)3 : 4Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of An organ pipe P1 closed at one end vibrating in its first overtone and another pipe P2 open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1 and P2 isa)1 : 2b)1 : 3c)3 : 8d)3 : 4Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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