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Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n₁ and the other with frequency n₂. The ratio n₁/n₂ is given by
- a)2
- b)4
- c)8
- d)1
Correct answer is option 'D'. Can you explain this answer?
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Given, two strings of same material with lengths L and 2L and radii 2r and r respectively are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n and the other with frequency n.
Let us assume that the tension in both the strings is T.
The frequency of vibration of a string is given by the formula:
n = (1/2L) √(T/μ) …(1)
where μ is the linear density of the string.
Let us calculate the linear density of the two strings.
The linear density of a string is given by the formula:
μ = m/L
where m is the mass of the string.
Let us assume that the density of the material of the two strings is ρ.
The mass of the first string of length L and radius 2r is given by:
m1 = πr^2Lρ
The mass of the second string of length 2L and radius r is given by:
m2 = πr^2(2L)ρ
Substituting the values of m1 and m2 in the formula for linear density, we get:
μ1 = m1/L = πr^2ρ
μ2 = m2/(2L) = πr^2ρ
We can see that the linear density of the two strings is the same.
Substituting the values of μ and L in equation (1), we get:
n1 = (1/2L) √(T/μ1)
n2 = (1/2(2L)) √(T/μ2)
Simplifying these equations, we get:
n1 = (1/2L) √(T/(πr^2ρ))
n2 = (1/4L) √(T/(πr^2ρ))
Dividing n1 by n2, we get:
n1/n2 = (2L)/(L) = 2
Therefore, the ratio of the frequencies of vibration of the two strings is 1:1.
Given, two strings of same material with lengths L and 2L and radii 2r and r respectively are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n and the other with frequency n.
Let us assume that the tension in both the strings is T.
The frequency of vibration of a string is given by the formula:
n = (1/2L) √(T/μ) …(1)
where μ is the linear density of the string.
Let us calculate the linear density of the two strings.
The linear density of a string is given by the formula:
μ = m/L
where m is the mass of the string.
Let us assume that the density of the material of the two strings is ρ.
The mass of the first string of length L and radius 2r is given by:
m1 = πr^2Lρ
The mass of the second string of length 2L and radius r is given by:
m2 = πr^2(2L)ρ
Substituting the values of m1 and m2 in the formula for linear density, we get:
μ1 = m1/L = πr^2ρ
μ2 = m2/(2L) = πr^2ρ
We can see that the linear density of the two strings is the same.
Substituting the values of μ and L in equation (1), we get:
n1 = (1/2L) √(T/μ1)
n2 = (1/2(2L)) √(T/μ2)
Simplifying these equations, we get:
n1 = (1/2L) √(T/(πr^2ρ))
n2 = (1/4L) √(T/(πr^2ρ))
Dividing n1 by n2, we get:
n1/n2 = (2L)/(L) = 2
Therefore, the ratio of the frequencies of vibration of the two strings is 1:1.
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Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n and the other with frequency n. The ratio n/n is given bya)2b)4c)8d)1Correct answer is option 'D'. Can you explain this answer?
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Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n and the other with frequency n. The ratio n/n is given bya)2b)4c)8d)1Correct answer is option 'D'. 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 Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n and the other with frequency n. The ratio n/n is given bya)2b)4c)8d)1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n and the other with frequency n. The ratio n/n is given bya)2b)4c)8d)1Correct answer is option 'D'. Can you explain this answer?.
Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n and the other with frequency n. The ratio n/n is given bya)2b)4c)8d)1Correct answer is option 'D'. 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 Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n and the other with frequency n. The ratio n/n is given bya)2b)4c)8d)1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n and the other with frequency n. The ratio n/n is given bya)2b)4c)8d)1Correct answer is option 'D'. Can you explain this answer?.
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Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n and the other with frequency n. The ratio n/n is given bya)2b)4c)8d)1Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n and the other with frequency n. The ratio n/n is given bya)2b)4c)8d)1Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n and the other with frequency n. The ratio n/n is given bya)2b)4c)8d)1Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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