Waves from two different sources overlap a particular point. The amplitude and frequency of the two waves are same.The ratio of the intensity when the two waves arrive in phase to that when they arrive `90^(@)` out of phase is :

Options

A. `1 : 1`
B. `sqrt2 : 1`
C. `2 : 1`
D. `4 : 1`

Answer

C

Explanation

When the two waves reach in phase, then the resultant amplitude =`a + a = 2a`
`therefore I_(1) = 4a^(2)`
When phase difference is `90^(@)`, resultant amplitude
` = [a^(2) + a^(2)]^(1/2) = sqrt 2a`
`therefore I_(2) = 2a^(2)`
`Rightarrow (I_(1))/(I_(2)) = (4a^(2))/(2a^(2)) = 2/1`