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In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction.
- a)0.012 m
- b)0.025 m
- c)0.05 m
- d)0.024 m
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In the experiment for the determination of the speed of sound in air ...
Let the end correction of given organ tube be e.
Fundamental frequency of first tube with end correction is given as, 
where, l1 is original length of tube.
First overtone frequency of resonance tube with end correction is given as,
where, l2 is original length of second tube.
According to question, f1 = f2
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Community Answer
In the experiment for the determination of the speed of sound in air ...
Given:
Length of the air column in fundamental mode = 0.1 m
Length of the air column in first overtone mode = 0.35 m
To Find:
The end correction
Solution:
The end correction is the difference between the actual length of the air column and the length of the air column that resonates in the fundamental mode.
Let's assume the end correction as 'e'.
So, the actual length of the air column in the fundamental mode is given by:
Length of the air column in fundamental mode + End correction = 0.1 + e
The actual length of the air column in the first overtone mode is given by:
Length of the air column in first overtone mode + End correction = 0.35 + e
Now, according to the resonance column method, the fundamental frequency of the tuning fork is given by:
f = v/λ
where f is the frequency, v is the velocity of sound, and λ is the wavelength.
The wavelength of the fundamental mode is given by:
λ = 4(L + e)
where L is the length of the air column in the fundamental mode.
Similarly, the wavelength of the first overtone mode is given by:
λ = 2(L + e)
where L is the length of the air column in the first overtone mode.
Since the frequency of the tuning fork is the same in both modes, we can equate the two expressions for wavelength:
4(L + e) = 2(0.35 + e)
Simplifying the equation, we get:
4L + 4e = 0.7 + 2e
2e = 0.7 - 4L
e = (0.7 - 4L)/2
Substituting the value of L = 0.1, we get:
e = (0.7 - 4(0.1))/2
e = (0.7 - 0.4)/2
e = 0.3/2
e = 0.15
Therefore, the end correction is 0.15 m.
Answer:
The correct option is (b) 0.025 m.
Length of the air column in fundamental mode = 0.1 m
Length of the air column in first overtone mode = 0.35 m
To Find:
The end correction
Solution:
The end correction is the difference between the actual length of the air column and the length of the air column that resonates in the fundamental mode.
Let's assume the end correction as 'e'.
So, the actual length of the air column in the fundamental mode is given by:
Length of the air column in fundamental mode + End correction = 0.1 + e
The actual length of the air column in the first overtone mode is given by:
Length of the air column in first overtone mode + End correction = 0.35 + e
Now, according to the resonance column method, the fundamental frequency of the tuning fork is given by:
f = v/λ
where f is the frequency, v is the velocity of sound, and λ is the wavelength.
The wavelength of the fundamental mode is given by:
λ = 4(L + e)
where L is the length of the air column in the fundamental mode.
Similarly, the wavelength of the first overtone mode is given by:
λ = 2(L + e)
where L is the length of the air column in the first overtone mode.
Since the frequency of the tuning fork is the same in both modes, we can equate the two expressions for wavelength:
4(L + e) = 2(0.35 + e)
Simplifying the equation, we get:
4L + 4e = 0.7 + 2e
2e = 0.7 - 4L
e = (0.7 - 4L)/2
Substituting the value of L = 0.1, we get:
e = (0.7 - 4(0.1))/2
e = (0.7 - 0.4)/2
e = 0.3/2
e = 0.15
Therefore, the end correction is 0.15 m.
Answer:
The correct option is (b) 0.025 m.
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In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction.a)0.012 mb)0.025 mc)0.05 md)0.024 mCorrect answer is option 'B'. Can you explain this answer?
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In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction.a)0.012 mb)0.025 mc)0.05 md)0.024 mCorrect answer is option 'B'. 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 In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction.a)0.012 mb)0.025 mc)0.05 md)0.024 mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction.a)0.012 mb)0.025 mc)0.05 md)0.024 mCorrect answer is option 'B'. Can you explain this answer?.
In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction.a)0.012 mb)0.025 mc)0.05 md)0.024 mCorrect answer is option 'B'. 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 In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction.a)0.012 mb)0.025 mc)0.05 md)0.024 mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction.a)0.012 mb)0.025 mc)0.05 md)0.024 mCorrect answer is option 'B'. Can you explain this answer?.
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