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When the waves y_{1} = A \sin \omega t and y_{2} = A \cos \omega t are superposed, then resultant amplitude will be:

Option: 1

\sqrt{2}A


Option: 2

\frac{1}{\sqrt{2}}A


Option: 3

A


Option: 4

2A


Answers (1)

best_answer

The resultant wave is given by:

y = y_{1} + y_{2} = A \sin \omega t + A \cos \omega t

= \sqrt 2 A (\sin \omega t \cdot \frac{1}{\sqrt 2}+ \cos \omega t \cdot \frac{1}{\sqrt 2})

= \sqrt 2 A (\sin \omega t \cos \frac{\pi }{4}+ \cos \omega t \sin \frac{\pi}{4})

= \sqrt 2 A \sin (\omega t + \frac{\pi}{4})

Hence the resultant amplitude = = \sqrt 2 A

Posted by

sudhir kumar

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