Figure shows two coherent sources `S_(1)` and `S_(2)` which emit sound of wavelength `lambda` in phase. The separation between the sources is `lambda.` A circular wire of large radius is placed in such a way that `S_(1)S_(2)` lies in its plane and the middle point of `S_(1)S_(2)` is at the centre of the wire. Find the angular positions `theta,` on the wire for which constructive interference takes place.

Answer

(i). `0^(@),60^(@),90^(@),120^(@),180^(@),240^(@),270^(@),300^(@),8`
(ii). `costheta=+-(1)/(8),+-(3)/(8),+-(5)/(8),+-(7)/(8)`

Explanation

The position of maxima where the path difference between two ways is integral multiple of `lamda`. And position of minima where the path difference between two ways is odd multiple of `lamda//2`