question_answer

Three harmonic waves having equal frequency \[\nu \]and same intensity\[{{I}_{0}}\], have phase angles \[0,\frac{\pi }{4}\] and \[-\frac{\pi }{4}\] respectively. When they are superimposed the intensity of the resultant wave is close to  [JEE MAIN Held on 09-01-2020 Morning]

A)  \[3{{I}_{0}}\]                         

B) \[~5.8{{I}_{0}}\]

C)  \[0.2{{I}_{0}}\]           

D)       \[{{I}_{0}}\]

Correct Answer: B

Solution :

[b]

\[{{I}_{0}}=C{{A}^{2}}\]

\[{{A}_{R}}=A+A\sqrt{2}=A\left( 1+\sqrt{2} \right)\]

\[{{I}_{R}}=CA_{R}^{2}\]

\[=C{{A}^{2}}{{\left( 1+\sqrt{2} \right)}^{2}}\]

\[{{I}_{R}}={{I}_{0}}{{\left( 1+\sqrt{2} \right)}^{2}}=5.8279{{I}_{0}}\]