The path difference between the two waves
`y_(1)=a_(1) sin(omega t-(2pi x)/(lambda)) and y(2)=a_(2) cos(omega t-(2pi x)/(lambda)+phi)` is

Options

A. `lambda/(2pi) (phi)`
B. `lambda/(2pi) (phi+pi/2)`
C. `(2pi)/lambda (phi-pi/2)`
D. `(2pi)/lambda (phi)`

Answer

B

Explanation

As `y_(2)=a_(2) cos (omega t-(2pi x)/lambda +phi)`
`=a_(2) sin [pi/2+(omega t-(2pi x)/lambda +phi)]`
Compare it with `y_(1)=a_(1) sin (omega t-(2pi x)/lambda)`
Phase difference `=(pi/2 +phi)`
`:.` Path difference `=lambda/(2pi)(pi/2 +phi)`.