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A standing wave is produced due to superposition of the incident wave and the wave reflected from a boundary.it is observed that the amplitude at antinode is 9 times that at node. The percentage of the incident intensity reflected from the boundary is. A)36 B)64% C)72% D)81%?
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A standing wave is produced due to superposition of the incident wave ...
Solution:
Given, amplitude at antinode = 9 amplitude at node
The amplitude of wave at antinode is given by A = 2a, where a is the amplitude of wave at each end.
Therefore, 2a = 9a/2
Solving this, we get a = A/6
Let the intensity of the incident wave be Ii and the intensity of the reflected wave be Ir.
The total intensity of the standing wave is given by I = Ii + Ir
The intensity at antinode is given by Iantinode = 4Ii
The intensity at node is given by Inode = Ii
Therefore, the ratio of the intensity at antinode to node is given by Iantinode/Inode = 4Ii/Ii = 4
The amplitude ratio is related to intensity ratio as follows:
(Aantinode/Anode)² = (Iantinode/Inode)
(2a/2a/√2)² = (4Ii/Ii)
9 = 8Ii/Ii
Ii = 9/8 Ir
Therefore, the percentage of the incident intensity reflected from the boundary is given by:
Ir/Ii x 100 = Ir/(9/8 Ir) x 100 = 88.89%
Hence, option D) 81% is not correct.
Therefore, the correct option is B) 64%.
Given, amplitude at antinode = 9 amplitude at node
The amplitude of wave at antinode is given by A = 2a, where a is the amplitude of wave at each end.
Therefore, 2a = 9a/2
Solving this, we get a = A/6
Let the intensity of the incident wave be Ii and the intensity of the reflected wave be Ir.
The total intensity of the standing wave is given by I = Ii + Ir
The intensity at antinode is given by Iantinode = 4Ii
The intensity at node is given by Inode = Ii
Therefore, the ratio of the intensity at antinode to node is given by Iantinode/Inode = 4Ii/Ii = 4
The amplitude ratio is related to intensity ratio as follows:
(Aantinode/Anode)² = (Iantinode/Inode)
(2a/2a/√2)² = (4Ii/Ii)
9 = 8Ii/Ii
Ii = 9/8 Ir
Therefore, the percentage of the incident intensity reflected from the boundary is given by:
Ir/Ii x 100 = Ir/(9/8 Ir) x 100 = 88.89%
Hence, option D) 81% is not correct.
Therefore, the correct option is B) 64%.
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A standing wave is produced due to superposition of the incident wave ...
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A standing wave is produced due to superposition of the incident wave and the wave reflected from a boundary.it is observed that the amplitude at antinode is 9 times that at node. The percentage of the incident intensity reflected from the boundary is. A)36 B)64% C)72% D)81%?
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A standing wave is produced due to superposition of the incident wave and the wave reflected from a boundary.it is observed that the amplitude at antinode is 9 times that at node. The percentage of the incident intensity reflected from the boundary is. A)36 B)64% C)72% D)81%? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A standing wave is produced due to superposition of the incident wave and the wave reflected from a boundary.it is observed that the amplitude at antinode is 9 times that at node. The percentage of the incident intensity reflected from the boundary is. A)36 B)64% C)72% D)81%? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A standing wave is produced due to superposition of the incident wave and the wave reflected from a boundary.it is observed that the amplitude at antinode is 9 times that at node. The percentage of the incident intensity reflected from the boundary is. A)36 B)64% C)72% D)81%?.
A standing wave is produced due to superposition of the incident wave and the wave reflected from a boundary.it is observed that the amplitude at antinode is 9 times that at node. The percentage of the incident intensity reflected from the boundary is. A)36 B)64% C)72% D)81%? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A standing wave is produced due to superposition of the incident wave and the wave reflected from a boundary.it is observed that the amplitude at antinode is 9 times that at node. The percentage of the incident intensity reflected from the boundary is. A)36 B)64% C)72% D)81%? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A standing wave is produced due to superposition of the incident wave and the wave reflected from a boundary.it is observed that the amplitude at antinode is 9 times that at node. The percentage of the incident intensity reflected from the boundary is. A)36 B)64% C)72% D)81%?.
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