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Two vibrating strings of same material stretched under same tension and vibrating with same frequency in the same overtone have radii 2r and r. Then the ratio of their lengths is :
- a)1 : 2
- b)1 : 4
- c)1 : 3
- d)2 : 3
Correct answer is option 'A'. Can you explain this answer?
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Two vibrating strings of same material stretched under same tension an...
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Given:
- Two vibrating strings of the same material
- Stretched under the same tension
- Vibrating with the same frequency
- Vibrating in the same overtone
- The radii of the strings are 2r and r
To find:
The ratio of their lengths
Explanation:
When a string is vibrating in an overtone, it forms standing waves. The fundamental frequency is the frequency at which the string vibrates in its first overtone.
Key concept:
The frequency of vibration of a string is inversely proportional to its length.
Analysis:
Let's assume the length of the string with radius 2r is L1, and the length of the string with radius r is L2.
Frequency of vibration:
Since both strings are vibrating with the same frequency, we can write:
v1/λ1 = v2/λ2
where v1 and v2 are the speeds of the waves on the two strings, and λ1 and λ2 are the wavelengths of the waves on the two strings.
Relation between wavelength and length:
The wavelength of a wave on a string is related to the length of the string by the formula:
λ = 2L/n
where λ is the wavelength, L is the length of the string, and n is the number of segments (or nodes) formed during the standing wave pattern.
Relation between speed, frequency, and wavelength:
The speed of a wave on a string is given by the formula:
v = fλ
where v is the speed of the wave, f is the frequency of vibration, and λ is the wavelength of the wave.
Substituting the values:
Using the above two formulas, we can write:
v1(2L1/n1) = v2(2L2/n2)
Since the strings are under the same tension and made of the same material:
The speed of the waves on both strings will be the same. Therefore, we can write:
v1 = v2
Canceling out the speeds:
We get:
2L1/n1 = 2L2/n2
Since both strings are vibrating in the same overtone:
The number of segments (n) will be the same for both strings. Therefore, we can write:
n1 = n2 = n
Canceling out the number of segments:
We get:
2L1 = 2L2
Dividing by 2:
L1 = L2
Conclusion:
The ratio of the lengths of the two strings is 1:1, or simply 1.
Answer:
The ratio of their lengths is 1:1, which is option 'A'.
- Two vibrating strings of the same material
- Stretched under the same tension
- Vibrating with the same frequency
- Vibrating in the same overtone
- The radii of the strings are 2r and r
To find:
The ratio of their lengths
Explanation:
When a string is vibrating in an overtone, it forms standing waves. The fundamental frequency is the frequency at which the string vibrates in its first overtone.
Key concept:
The frequency of vibration of a string is inversely proportional to its length.
Analysis:
Let's assume the length of the string with radius 2r is L1, and the length of the string with radius r is L2.
Frequency of vibration:
Since both strings are vibrating with the same frequency, we can write:
v1/λ1 = v2/λ2
where v1 and v2 are the speeds of the waves on the two strings, and λ1 and λ2 are the wavelengths of the waves on the two strings.
Relation between wavelength and length:
The wavelength of a wave on a string is related to the length of the string by the formula:
λ = 2L/n
where λ is the wavelength, L is the length of the string, and n is the number of segments (or nodes) formed during the standing wave pattern.
Relation between speed, frequency, and wavelength:
The speed of a wave on a string is given by the formula:
v = fλ
where v is the speed of the wave, f is the frequency of vibration, and λ is the wavelength of the wave.
Substituting the values:
Using the above two formulas, we can write:
v1(2L1/n1) = v2(2L2/n2)
Since the strings are under the same tension and made of the same material:
The speed of the waves on both strings will be the same. Therefore, we can write:
v1 = v2
Canceling out the speeds:
We get:
2L1/n1 = 2L2/n2
Since both strings are vibrating in the same overtone:
The number of segments (n) will be the same for both strings. Therefore, we can write:
n1 = n2 = n
Canceling out the number of segments:
We get:
2L1 = 2L2
Dividing by 2:
L1 = L2
Conclusion:
The ratio of the lengths of the two strings is 1:1, or simply 1.
Answer:
The ratio of their lengths is 1:1, which is option 'A'.
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Two vibrating strings of same material stretched under same tension and vibrating with same frequency in the same overtone have radii 2r and r. Then the ratio of their lengths is :a)1 : 2b)1 : 4c)1 : 3d)2 : 3Correct answer is option 'A'. Can you explain this answer?
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Two vibrating strings of same material stretched under same tension and vibrating with same frequency in the same overtone have radii 2r and r. Then the ratio of their lengths is :a)1 : 2b)1 : 4c)1 : 3d)2 : 3Correct answer is option 'A'. 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 Two vibrating strings of same material stretched under same tension and vibrating with same frequency in the same overtone have radii 2r and r. Then the ratio of their lengths is :a)1 : 2b)1 : 4c)1 : 3d)2 : 3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two vibrating strings of same material stretched under same tension and vibrating with same frequency in the same overtone have radii 2r and r. Then the ratio of their lengths is :a)1 : 2b)1 : 4c)1 : 3d)2 : 3Correct answer is option 'A'. Can you explain this answer?.
Two vibrating strings of same material stretched under same tension and vibrating with same frequency in the same overtone have radii 2r and r. Then the ratio of their lengths is :a)1 : 2b)1 : 4c)1 : 3d)2 : 3Correct answer is option 'A'. 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 Two vibrating strings of same material stretched under same tension and vibrating with same frequency in the same overtone have radii 2r and r. Then the ratio of their lengths is :a)1 : 2b)1 : 4c)1 : 3d)2 : 3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two vibrating strings of same material stretched under same tension and vibrating with same frequency in the same overtone have radii 2r and r. Then the ratio of their lengths is :a)1 : 2b)1 : 4c)1 : 3d)2 : 3Correct answer is option 'A'. Can you explain this answer?.
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Two vibrating strings of same material stretched under same tension and vibrating with same frequency in the same overtone have radii 2r and r. Then the ratio of their lengths is :a)1 : 2b)1 : 4c)1 : 3d)2 : 3Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Two vibrating strings of same material stretched under same tension and vibrating with same frequency in the same overtone have radii 2r and r. Then the ratio of their lengths is :a)1 : 2b)1 : 4c)1 : 3d)2 : 3Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Two vibrating strings of same material stretched under same tension and vibrating with same frequency in the same overtone have radii 2r and r. Then the ratio of their lengths is :a)1 : 2b)1 : 4c)1 : 3d)2 : 3Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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