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Three harmonic waves having equal freque...

Three harmonic waves having equal frequency and same intensity `I_(0)` have phase angle`- phi, 0 ` & `phi` respectively.When they are superimposed internsity of the resultant wave becomes `4I_(0)`. Find `phi`

A

0

B

`(pi)/( 6)`

C

`( pi)/( 2)`

D

`( pi)/( 3)`

Text Solution

Verified by Experts

`y_(1) = A sin (omega t - phi ) ` `( I_(0) propA^(2))`
`y_(2) = A sin omega t , y_(3) =A sin (omega t + phi ) , y =y_(1) + y_(2) +y_(3)`
`y = A sin omega t cos phi -A cos omega t sin phi + A sin omega t cos phi +Acosomegat sin phi + A sin omegat `
`y = 2A sin omega t cos phi + A sin omega t `
If `cos phi =(1)/( 2)`
They `y = 2Asin omega t ` `I prop ( 2A)^(2) rArr I prop 4A^(2) rArr I = 4I_(0)`
Here `I=4I_(0)`
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