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A rod is clamped at both of its ends and stationary longitudinal waves are produced in it. In first experiment, the rod has a total of 4 nodes with amplitude of each anti-node to be 1 mm. In other experiment, the rod has a total of 6 nodes with amplitude of each anti node to be 2mm. The energy of vibrations in the rod in two cases is E1 and E2 respectively. Write value of E1/E2.
Correct answer is '0.9'. Can you explain this answer?
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A rod is clamped at both of its ends and stationary longitudinal waves...
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A rod is clamped at both of its ends and stationary longitudinal waves...
Explanation:
Hence, the value of E1/E2 is 0.9.
- When stationary longitudinal waves are produced in the rod, energy is stored in the form of elastic potential energy.
- The energy of vibrations in the rod is directly proportional to the square of the amplitude of vibration at the anti-nodes.
- Let the length of the rod be L and the speed of the wave be v.
- For the first experiment, the number of nodes is 4, which means there are 5 segments of the rod.
- The wavelength of the wave is given by λ = 2L/5.
- Let the amplitude of the vibration at the anti-nodes be A.
- The energy of vibrations in the rod is given by E1 = (1/2) * (density of the rod) * (cross-sectional area of the rod) * (A^2) * (π^2) * (v^2) * (5/2) * (1/λ^2).
- For the second experiment, the number of nodes is 6, which means there are 7 segments of the rod.
- The wavelength of the wave is given by λ = 2L/7.
- Let the amplitude of the vibration at the anti-nodes be 2A.
- The energy of vibrations in the rod is given by E2 = (1/2) * (density of the rod) * (cross-sectional area of the rod) * (4A^2) * (π^2) * (v^2) * (7/2) * (1/λ^2).
- Dividing E1 by E2, we get E1/E2 = (5/7) * (1/A^2).
- Substituting the given values, we get E1/E2 = (5/7) * (1/1^2) / (1/2^2) = 0.9.
Hence, the value of E1/E2 is 0.9.
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A rod is clamped at both of its ends and stationary longitudinal waves are produced in it. In first experiment, the rod has a total of 4 nodes with amplitude of each anti-node to be 1 mm. In other experiment, the rod has a total of 6 nodes with amplitude of each anti node to be 2mm. The energy of vibrations in the rod in two cases is E1and E2respectively. Write value of E1/E2.Correct answer is '0.9'. Can you explain this answer?
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A rod is clamped at both of its ends and stationary longitudinal waves are produced in it. In first experiment, the rod has a total of 4 nodes with amplitude of each anti-node to be 1 mm. In other experiment, the rod has a total of 6 nodes with amplitude of each anti node to be 2mm. The energy of vibrations in the rod in two cases is E1and E2respectively. Write value of E1/E2.Correct answer is '0.9'. 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 rod is clamped at both of its ends and stationary longitudinal waves are produced in it. In first experiment, the rod has a total of 4 nodes with amplitude of each anti-node to be 1 mm. In other experiment, the rod has a total of 6 nodes with amplitude of each anti node to be 2mm. The energy of vibrations in the rod in two cases is E1and E2respectively. Write value of E1/E2.Correct answer is '0.9'. 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 rod is clamped at both of its ends and stationary longitudinal waves are produced in it. In first experiment, the rod has a total of 4 nodes with amplitude of each anti-node to be 1 mm. In other experiment, the rod has a total of 6 nodes with amplitude of each anti node to be 2mm. The energy of vibrations in the rod in two cases is E1and E2respectively. Write value of E1/E2.Correct answer is '0.9'. Can you explain this answer?.
A rod is clamped at both of its ends and stationary longitudinal waves are produced in it. In first experiment, the rod has a total of 4 nodes with amplitude of each anti-node to be 1 mm. In other experiment, the rod has a total of 6 nodes with amplitude of each anti node to be 2mm. The energy of vibrations in the rod in two cases is E1and E2respectively. Write value of E1/E2.Correct answer is '0.9'. 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 rod is clamped at both of its ends and stationary longitudinal waves are produced in it. In first experiment, the rod has a total of 4 nodes with amplitude of each anti-node to be 1 mm. In other experiment, the rod has a total of 6 nodes with amplitude of each anti node to be 2mm. The energy of vibrations in the rod in two cases is E1and E2respectively. Write value of E1/E2.Correct answer is '0.9'. 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 rod is clamped at both of its ends and stationary longitudinal waves are produced in it. In first experiment, the rod has a total of 4 nodes with amplitude of each anti-node to be 1 mm. In other experiment, the rod has a total of 6 nodes with amplitude of each anti node to be 2mm. The energy of vibrations in the rod in two cases is E1and E2respectively. Write value of E1/E2.Correct answer is '0.9'. Can you explain this answer?.
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