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