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A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________. -
Correct answer is between '0.62,0.63'. Can you explain this answer?
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A stationary tuning fork is in resonance with an air column in a pipe....
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A stationary tuning fork is in resonance with an air column in a pipe....
Understanding the Scenario
When a stationary tuning fork is in resonance with an air column in a pipe, the length of the pipe supports a specific frequency. If the tuning fork moves, it alters the effective frequency perceived by the pipe, requiring a change in the pipe's length for resonance to be maintained.
Key Parameters
- Speed of Sound (v): 320 m/s
- Speed of Tuning Fork (u): 2 m/s
Frequency Change Due to Motion
The frequency observed by the pipe changes when the source (tuning fork) is moving. The new frequency (f') can be determined using the Doppler effect:
- f' = f * (v + u) / v
Since the tuning fork is moving toward the open end of the pipe, the effective frequency increases.
Calculating the Required Change in Length
The length of the pipe (L) is related to the frequency (f) and speed of sound (v):
- f = v / (4L) for the fundamental frequency
When the tuning fork moves, the new frequency must correspond to a new length (L'):
- f' = v / (4L')
Setting the two frequency equations equal gives:
- f * (v + u) / v = v / (4L')
This implies that the new length must satisfy:
- L' = L * (v / (v + u))
Percentage Change in Length
The percentage change in the length of the pipe can be calculated as:
- Percentage Change = [(L - L') / L] * 100
Substituting L' gives:
- Percentage Change = [(u / (v + u)) * 100]
Plugging in the values:
- Percentage Change = [(2 / (320 + 2)) * 100] = 0.62%
Conclusion
Therefore, the smallest value of the percentage change required in the length of the pipe for resonance is between 0.62% and 0.63%.
When a stationary tuning fork is in resonance with an air column in a pipe, the length of the pipe supports a specific frequency. If the tuning fork moves, it alters the effective frequency perceived by the pipe, requiring a change in the pipe's length for resonance to be maintained.
Key Parameters
- Speed of Sound (v): 320 m/s
- Speed of Tuning Fork (u): 2 m/s
Frequency Change Due to Motion
The frequency observed by the pipe changes when the source (tuning fork) is moving. The new frequency (f') can be determined using the Doppler effect:
- f' = f * (v + u) / v
Since the tuning fork is moving toward the open end of the pipe, the effective frequency increases.
Calculating the Required Change in Length
The length of the pipe (L) is related to the frequency (f) and speed of sound (v):
- f = v / (4L) for the fundamental frequency
When the tuning fork moves, the new frequency must correspond to a new length (L'):
- f' = v / (4L')
Setting the two frequency equations equal gives:
- f * (v + u) / v = v / (4L')
This implies that the new length must satisfy:
- L' = L * (v / (v + u))
Percentage Change in Length
The percentage change in the length of the pipe can be calculated as:
- Percentage Change = [(L - L') / L] * 100
Substituting L' gives:
- Percentage Change = [(u / (v + u)) * 100]
Plugging in the values:
- Percentage Change = [(2 / (320 + 2)) * 100] = 0.62%
Conclusion
Therefore, the smallest value of the percentage change required in the length of the pipe for resonance is between 0.62% and 0.63%.
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A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________. -Correct answer is between '0.62,0.63'. Can you explain this answer?
Question Description
A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________. -Correct answer is between '0.62,0.63'. 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 A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________. -Correct answer is between '0.62,0.63'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________. -Correct answer is between '0.62,0.63'. Can you explain this answer?.
A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________. -Correct answer is between '0.62,0.63'. 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 A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________. -Correct answer is between '0.62,0.63'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________. -Correct answer is between '0.62,0.63'. Can you explain this answer?.
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A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________. -Correct answer is between '0.62,0.63'. Can you explain this answer?, a detailed solution for A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________. -Correct answer is between '0.62,0.63'. Can you explain this answer? has been provided alongside types of A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms−1 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms−1, the smallest value of the percentage change required in the length of the pipe is ____________. -Correct answer is between '0.62,0.63'. Can you explain this answer? theory, EduRev gives you an
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