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Question
Two periodic waves of amplitudes A1 and A2 pass thorough a region. If A1 > A2, the difference in the maximum and minimum resultant amplitude possible is
Options
2A1
2A2
A1 + A2
A1 − A2
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Solution
2A2
We know resultant amplitude is given by
\[A_{net} = \sqrt{A_1^2 + A_2^2 + 2 A_1 A_2 \cos\phi}\] For maximum resultant amplitude \[A_\max = A_1 + A_2\] For minimum resultant amplitude \[A_\min = A_1 - A_2\]
So, the difference between Amax and Amin is
\[A_\max - A_\min = A_1 + A_2 - A_1 + A_2 = 2 A_2\]
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