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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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Given:
- Two vibrating strings of the same material are stretched under the same tension.
- The strings are vibrating with the same frequency in the same overtone.
- The radii of the strings are 2r and r.
To find:
The ratio of their lengths.
Solution:
Let's assume the lengths of the strings are L1 and L2, and the radii are r1 = 2r and r2 = r.
Step 1: Relationship between length and radius
The length of a string is directly proportional to the square of its radius. So we can write:
L ∝ r^2
Step 2: Relationship between length and frequency
The fundamental frequency of a vibrating string is inversely proportional to its length. So we can write:
f ∝ 1/L
Step 3: Relationship between length and tension
The fundamental frequency of a vibrating string is directly proportional to the square root of the tension. So we can write:
f ∝ √T
Step 4: Relationship between radius and tension
The tension in a string is directly proportional to the square of its radius. So we can write:
T ∝ r^2
Step 5: Combining the relationships
Using the relationships derived in steps 1-4, we can write:
f1/f2 = (L2/L1) * (√T1/√T2) * (r2^2/r1^2)
Since the strings are vibrating with the same frequency in the same overtone, f1 = f2, and we can simplify the equation to:
L2/L1 = (r2^2/r1^2)
Substituting the given values of r1 = 2r and r2 = r, we get:
L2/L1 = (r^2)/(2r)^2 = 1/4
Therefore, the ratio of the lengths of the strings is 1:4, which corresponds to option 'A'.
Answer:
The ratio of the lengths of the strings is 1:4.
- Two vibrating strings of the same material are stretched under the same tension.
- The strings are vibrating with the same frequency in the same overtone.
- The radii of the strings are 2r and r.
To find:
The ratio of their lengths.
Solution:
Let's assume the lengths of the strings are L1 and L2, and the radii are r1 = 2r and r2 = r.
Step 1: Relationship between length and radius
The length of a string is directly proportional to the square of its radius. So we can write:
L ∝ r^2
Step 2: Relationship between length and frequency
The fundamental frequency of a vibrating string is inversely proportional to its length. So we can write:
f ∝ 1/L
Step 3: Relationship between length and tension
The fundamental frequency of a vibrating string is directly proportional to the square root of the tension. So we can write:
f ∝ √T
Step 4: Relationship between radius and tension
The tension in a string is directly proportional to the square of its radius. So we can write:
T ∝ r^2
Step 5: Combining the relationships
Using the relationships derived in steps 1-4, we can write:
f1/f2 = (L2/L1) * (√T1/√T2) * (r2^2/r1^2)
Since the strings are vibrating with the same frequency in the same overtone, f1 = f2, and we can simplify the equation to:
L2/L1 = (r2^2/r1^2)
Substituting the given values of r1 = 2r and r2 = r, we get:
L2/L1 = (r^2)/(2r)^2 = 1/4
Therefore, the ratio of the lengths of the strings is 1:4, which corresponds to option 'A'.
Answer:
The ratio of the lengths of the strings is 1:4.
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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 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 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 NEET 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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