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Question
Two waves represented by \[y = a\sin\left( \omega t - kx \right)\] and \[y = a\cos\left( \omega t - kx \right)\] \[y = a\cos\left( \omega t - kx \right)\] are superposed. The resultant wave will have an amplitude
Options
a
\[\sqrt{2}a\]
2a
0.
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Solution
\[\sqrt{2}a\]
We know that the resultant of the amplitude is given by
\[R_{net} = \sqrt{A_1^2 + A_2^2 + 2 A_1 A_2 \cos\phi}\]
For the particular case, we can write
\[= \sqrt{a^2 + a^2 + 2 a^2 \cos\frac{\pi}{2}}\]
\[ = \sqrt{2}a\]
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