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Two coherent waves are described by the ...

Two coherent waves are described by the expressions.
`E_(1)=E_(0)sin((2pix_(1))/(lambda)-2pift+(pi)/(6))`
`E_(2)=E_(0)sin((2pix_(2))/(lambda)-2pift+(pi)/(8))`
Determine the relationship between `x_(1)`and`x_(2)`that produces constructive interference when the two waves are superposed.

Text Solution

Verified by Experts

The correct Answer is:
`(n-(1)/(48))lambda=x_(1)-x_(2)`
`phi_(1)=((2pix_(1))/(lambda)-2pift+pi//6) &phi_(2)=((2pix_(2))/(lambda)-2pift+pi//8)`
For contructive interference
`phi_(1)-phi_(2)=2npi rArr so,(2pi)/(lambda)(x_(1)-x_(2))+(pi)/(6)-(pi)/(8)=2npi`
`(2pi)/(lambda)(x_(1)-x_(2))+(pi)/(24)=2npi rArr(2pi)/(lambda)(x_(1)-x_(2))=2npi-(pi)/(24)`
`x_(1)-x_(2)=(n-(1)/(48))lambda`
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