Two speakers separeted by some distance emit sound of the same frequency. At some point `P` the intensity due to each speaker separately is `I_(o)`. The path difference from `P` to one of the speakers is `(1)/(2) lambda` greater than that from `P` to the other speaker. What is the intensity at `P` if
(a) the speakers are coherent and in phase,
(b) the speakers are incoherent, and
(c ) the speakers are coherent but have a phase different of `180^(@)`?

Answer

A, B, C, D

Explanation

`Delta phi_(1) = ((2 pi)/(lambda)) Delta x = ((2 pi)/(lambda)) (lambda)/(2) = pi`
(a) `Delta phi_(net) = Delta phi_(1) + Delta phi_(2)`
`= pi + 0`
`= pi`
So, they will interfere destructively and
`I_(net) = I_(1) = 0`
(b) No interface will take place. Hence,
`i_(net) = I_(1) + I_(2) = 2l_(o)`
(c ) `Delta phi_(net) = Delta phi_(1) +- Delta phi_(2)`
`= 2 pi` or `0` (as `Delta phi_(2) = pi`)
In both conditions, they interfere
constructively.Hence,
`I = I_(max) = 4l_(o)`