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A cylindrical tube, open at both ends, has a fundamental frequency, f, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :
- a)f
- b)f/3
- c)3f/4
- d)2f
Correct answer is option 'A'. Can you explain this answer?
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A cylindrical tube, open at both ends, has a fundamental frequency, f,...
The fundamental frequency of open tube
That of closed pipe
According to the problem 
From equations (i) and (iii)
Most Upvoted Answer
A cylindrical tube, open at both ends, has a fundamental frequency, f,...
Fundamental frequency and resonance in a cylindrical tube
Fundamental frequency:
The fundamental frequency of a vibrating object is the lowest frequency at which it can vibrate and produce a standing wave pattern. In the case of a cylindrical tube open at both ends, the fundamental frequency is given by the formula:
f = (v/2L)
where f is the fundamental frequency, v is the speed of sound in air, and L is the length of the tube.
Resonance in a cylindrical tube:
When a sound wave is produced in a cylindrical tube open at both ends, it can travel back and forth between the two ends and create a standing wave pattern. This standing wave pattern is characterized by nodes and antinodes. The nodes are points of no displacement, while the antinodes are points of maximum displacement.
Effect of dipping the tube in water:
When the cylindrical tube is dipped vertically in water so that half of it is in water, the effective length of the tube changes. The length of the air column above the water becomes half of the original length, while the length of the air column below the water remains the same.
Explanation of the correct answer:
When the tube is dipped in water, the effective length of the air column above the water becomes half of the original length. As a result, the fundamental frequency of the air column also changes.
According to the formula for the fundamental frequency, f = (v/2L), if the length L is halved, then the fundamental frequency will be doubled. Therefore, the fundamental frequency of the air column when half of the tube is dipped in water will be twice the original fundamental frequency.
Since the question states that the fundamental frequency in air is 'f', the fundamental frequency of the air column when half of the tube is dipped in water will be '2f'.
Therefore, the correct answer is option 'A', which states that the fundamental frequency of the air-column is f.
Fundamental frequency:
The fundamental frequency of a vibrating object is the lowest frequency at which it can vibrate and produce a standing wave pattern. In the case of a cylindrical tube open at both ends, the fundamental frequency is given by the formula:
f = (v/2L)
where f is the fundamental frequency, v is the speed of sound in air, and L is the length of the tube.
Resonance in a cylindrical tube:
When a sound wave is produced in a cylindrical tube open at both ends, it can travel back and forth between the two ends and create a standing wave pattern. This standing wave pattern is characterized by nodes and antinodes. The nodes are points of no displacement, while the antinodes are points of maximum displacement.
Effect of dipping the tube in water:
When the cylindrical tube is dipped vertically in water so that half of it is in water, the effective length of the tube changes. The length of the air column above the water becomes half of the original length, while the length of the air column below the water remains the same.
Explanation of the correct answer:
When the tube is dipped in water, the effective length of the air column above the water becomes half of the original length. As a result, the fundamental frequency of the air column also changes.
According to the formula for the fundamental frequency, f = (v/2L), if the length L is halved, then the fundamental frequency will be doubled. Therefore, the fundamental frequency of the air column when half of the tube is dipped in water will be twice the original fundamental frequency.
Since the question states that the fundamental frequency in air is 'f', the fundamental frequency of the air column when half of the tube is dipped in water will be '2f'.
Therefore, the correct answer is option 'A', which states that the fundamental frequency of the air-column is f.
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A cylindrical tube, open at both ends, has a fundamental frequency, f, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :a)fb)f/3c)3f/4d)2fCorrect answer is option 'A'. Can you explain this answer?
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A cylindrical tube, open at both ends, has a fundamental frequency, f, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :a)fb)f/3c)3f/4d)2fCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A cylindrical tube, open at both ends, has a fundamental frequency, f, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :a)fb)f/3c)3f/4d)2fCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A cylindrical tube, open at both ends, has a fundamental frequency, f, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :a)fb)f/3c)3f/4d)2fCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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