Two waves of nearly same amplitude , same frequency travelling with same velocity are superimposing to give phenomenon of interference . If `a_(1)` and `a_(2)` be their respectively amplitudes , `omega` be the frequency for both , `v` be the velocity for both and `Delta phi` is the phase difference between the two waves then ,

Options

A. the resultant intensity varies periodically with time and distance.
B. the resulting intensity with `(I_(min))/(I_(max)) = (a_(1) - a_(2))/(a_(1) + a_(2))^(2)` is obtained.
C. both the waves must have been travelling in the same direction and must be coherent.
D. `I_(R) = I_(1) + I_(2) + 2 sqrt(I_(1) I_(2)) cos ( Delta phi)`, where constructive interference is obtained for path difference that are odd multiple of `1//2 lambda` and destructive interference is obtained for path difference that are even multiple of `1//2 lambda`.

Answer

C

Explanation

This is the case of sustained interference in which position of maxima and minima remains fixed all over the screen.
`(I_(min))/(I_(max)) = (( a_(1) - a_(2))/( a_(1) + a_(2)))^(2) `
And both waves must have been travelling in the same direction with a constant phase difference ( condition for coherence)