Figure (16-E7) shows two coherent sources S1 and S2 which emit sound of wavelength λ in phase. The separation between the sources is 3λ. A circular wire of large radius is placed in such a way that S1S2 lies in its plane and the middle point of S1S2 is at the centre of the wire. Find the angular positions θ on the wire for which constructive takes place.
Let the sound waves from the two coherent sources S1 and S2 reach the point P.
Rework
From the figure, we find that:
Path difference between the sound waves reaching point P is given by:
Suppose, for constructive interference, this path difference be made equal to the integral multiple of 
.
Hence,
Where, n = 0, 1, 2…
⇒ θ = 0°, 48.2°, 70.5°and 90° are similar points in other quadrants.
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