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Question
Two sine waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is 120°. The resultant amplitude will be
Options
A
2A
4A
\[\sqrt{2}A\]
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Solution
A
We know the resultant amplitude is given by
\[R_{net} = \sqrt{A^2 + A^2 + 2 A^2 \cos 120 ^\circ\ } (\phi = 120^\circ\ )\]
\[ = \sqrt{2 A^2 - A^2} \left[ \because \cos 120 ^\circ= \frac{- 1}{2} \right]\]
\[ = A\]
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