Two coherent sources are placed at the corners of a rectangular track of sides `3m` & `4 m`. The source `S_(1)` lags `S_(2)` by phase angle `pi`. A detector is moved along path `ABC`. Then find:

The ratio of total number of minima detected on line `AB` to the total number of minima on line `BC` is `(P)/(Q)` (in lowest form). Find `P.Q`
[Velocity of sound `= 330 m//s,` Frequency of sources `S_(1)` and `S_(2) = 165 Hz`]

Answer

6

Explanation

(i) Phase angle for `S_(1) , theta_(1) = (omegat - kx_(1))` and for `S_(2), theta_(2) = (omegat - kx_(2) + pi)`
`theta_(1) = theta_(2)`
`kx_(2) - kx_(1) = pi , (":' (V)/(n) = lambda = (330)/(165) = 2)`
`2x_(2) - 2x_(1) = lambda`
So `x_(2) - x_(1) = 1`
on the path `ABC` it is possible at `B` where `x_(2) = 4` & `x_(1) = 3`
Ans `=` At `B` on `ABC`
(ii) At `A` phase difference is `4pi` and at `B` it is zero so minima in between these will be at `pi` & `3pi` phase difference so total `2` minima.
At `C` phase differrence is `6pi` so - between `B` & `C` there will be minima at `1pi, 3pi` & `5pi` phase difference total `3` minima
ratio `= 2 : 3`