Three harmonic waves having equal frequency v and same intensity I _ 0 , have phase angles 0, (π)/(4) and - (π)/(4) respectively. When they are superimposed the intensity of the resultant wave is close to:

Correct answer: A. 5.8 I _ 0 A _ R = ( 2 + 1)A I _ R = ( 2 + 1) ^ 2 I _ 0 = (3 + 2 2 ) I _ 0 = 5.8 I _ 0

JEE Main 20209 JanuaryMorning Shift

Exam: JEE Main
Year: 2020
Date: 9 January
Shift: Morning Shift
Subject: Physics
Chapter: Waves and Sound

JEE Main 2020 · 9 January · Morning Shift · Physics · Waves and Sound

Three harmonic waves having equal frequency v and same intensity I...

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: Three harmonic waves having equal frequency v and same intensity I _ 0 , have phase angles 0, (π)/(4) and - (π)/(4)

Three harmonic waves having equal frequency v and same intensity I _ 0 , have phase angles 0, (π)/(4) and - (π)/(4)

Options

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

Correct answer

A. $5.8{I}_{0}$

Step-by-step solution

{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}

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