Two waves of equal amplitude and frequency interfere each other. The ratio of intensity when the two waves arrive in phase to that when they arrive `90^@` out of phase is

Options

A. `2:1`
B. `1:1`
C. `sqrt(2):1`
D. `4:1`

Answer

A

Explanation

For same phase, phas diff =0
`:. I_("max")=I_(2)+I_(2) +sqrt(I_(1)I_(2)) 2 cos (alpha_(1)-alpha_(2))`
`I+I+2I=4I " "...(i)`
For phae diff. `=90^(@)`
`I_("min")=I_(1)I_(2)+sqrt(I_(1)I_(2)) 2 cos 90`
`=2I`
Thus, `(I_("max"))/(I_("min"))=(4I)/(2I)=(2)/(I) " "...(ii)`