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The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is _____ cm.
Correct answer is '80'. Can you explain this answer?
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The first overtone frequency of an open organ pipe is equal to the fun...
Given, f1 = f2
l1 = 4l2 = 80 cm
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The first overtone frequency of an open organ pipe is equal to the fun...
Given:
The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe.
Length of the closed organ pipe = 20 cm.
To find:
Length of the open organ pipe.
Solution:
Let's analyze the problem step by step.
1. Understanding the concept of overtones:
- Overtones are higher frequency vibrations that occur along with the fundamental frequency in a musical instrument.
- The fundamental frequency is the lowest frequency produced by the instrument, and overtones are integer multiples of the fundamental frequency.
- The first overtone is the second harmonic, which is two times the frequency of the fundamental frequency.
2. Understanding the concept of open and closed organ pipes:
- An open organ pipe is open at both ends, allowing air to move freely.
- A closed organ pipe is closed at one end and open at the other end.
3. Relationship between length and frequency:
- In a closed organ pipe, the fundamental frequency (f1) is given by:
f1 = v / (4L), where v is the speed of sound and L is the length of the pipe.
- The first overtone frequency (f2) of an open organ pipe is given by:
f2 = v / (2L), where L is the length of the pipe.
- According to the given statement, f2 = f1.
4. Solving the equation:
- Substituting the values of f1 and f2:
v / (2L) = v / (4L)
- Cross-multiplying and simplifying:
2L = 4L
L = 2L
- We know that the length of the closed organ pipe is 20 cm.
- Therefore, the length of the open organ pipe is 2 * 20 = 40 cm.
5. Answer:
The length of the open organ pipe is 40 cm.
However, the correct answer mentioned is 80 cm, which seems to be a discrepancy. If the given answer is correct, it may be due to a typo or a mistake in the question itself.
The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe.
Length of the closed organ pipe = 20 cm.
To find:
Length of the open organ pipe.
Solution:
Let's analyze the problem step by step.
1. Understanding the concept of overtones:
- Overtones are higher frequency vibrations that occur along with the fundamental frequency in a musical instrument.
- The fundamental frequency is the lowest frequency produced by the instrument, and overtones are integer multiples of the fundamental frequency.
- The first overtone is the second harmonic, which is two times the frequency of the fundamental frequency.
2. Understanding the concept of open and closed organ pipes:
- An open organ pipe is open at both ends, allowing air to move freely.
- A closed organ pipe is closed at one end and open at the other end.
3. Relationship between length and frequency:
- In a closed organ pipe, the fundamental frequency (f1) is given by:
f1 = v / (4L), where v is the speed of sound and L is the length of the pipe.
- The first overtone frequency (f2) of an open organ pipe is given by:
f2 = v / (2L), where L is the length of the pipe.
- According to the given statement, f2 = f1.
4. Solving the equation:
- Substituting the values of f1 and f2:
v / (2L) = v / (4L)
- Cross-multiplying and simplifying:
2L = 4L
L = 2L
- We know that the length of the closed organ pipe is 20 cm.
- Therefore, the length of the open organ pipe is 2 * 20 = 40 cm.
5. Answer:
The length of the open organ pipe is 40 cm.
However, the correct answer mentioned is 80 cm, which seems to be a discrepancy. If the given answer is correct, it may be due to a typo or a mistake in the question itself.
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The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is _____ cm.Correct answer is '80'. Can you explain this answer?
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The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is _____ cm.Correct answer is '80'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is _____ cm.Correct answer is '80'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is _____ cm.Correct answer is '80'. Can you explain this answer?.
The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is _____ cm.Correct answer is '80'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is _____ cm.Correct answer is '80'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is _____ cm.Correct answer is '80'. Can you explain this answer?.
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