Two coherent narrow slits emitting sound of wavelength λ in the same phase are placed parallel to each other at a small separation of 2λ. The sound is detected by moving a detector on the screen ∑ at a distance D(>>λ) from the slit S1 as shown in figure (16-E6). Find the distance x such that the intensity at P is equal to the intensity at O.



Given:


S1 & S2 are in the same phase. At O, there will be maximum intensity.
There will be maximum intensity at P.


Capture.PNG


and are right-angled triangles.
So,





( Is small and can be neglected)





.
So,









When n=1,


(1st order).


When n=2,


x=0 (2nd order).


So, when, the intensity at P is equal to the intensity at O.


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