Question 55 of 142

Three harmonic waves having equal frequency $v$ and same intensity ${I}_{0}$ , have phase angles $0,\dfrac{\pi }{4}$ and $-\dfrac{\pi }{4}$ respectively. When they are superimposed the intensity of the resultant wave is close to:

A$5.8{I}_{0}$B$0.2{I}_{0}$C$3{I}_{0}$D${I}_{0}$

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Answer: (A) $5.8{I}_{0}$

${A}_{R}=\left(\sqrt{2}+1\right)A$
${I}_{R}={\left(\sqrt{2}+1\right)}^{2}{I}_{0}$
$=\left(3+2\sqrt{2}\right){I}_{0}=5.8{I}_{0}$