Two coherent narrow slits emitting sound of wavelength `lambda` in the same phase are placed parallel to each other at a small separation of `2 lambda`. The sound is detected by moving a detector on the screen at a distance `D ( gt gt lambda)` from the slit `S_1` as shown in figure. Find the distance y such that the intensity at P is equal to intensity at O.

Explanation

Let `Deltax = lambda` at angle `theta` (see fig) Path difference between the waves is `Deltax = 2lambdacos theta`
`:. 2lambda cos theta = lambda (Deltax =lambda) or theta = 60^@`
Now, `PO = S_1O cot 30^@ or y = sqrt 3D`