Figure 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 S₁ and S₂ lies in its plane and the middle point of S₁, S₂ is at the centre of the wire. Find the value of cosθ for which constructive interference takes place. Choose the option containing the correct final result.

Question

G1 Physics · Accepted Answer

Step 1: Add the waves as phasors. For two amplitudes A₁,A₂ with phase difference φ, A² = A₁² + A₂² + 2A₁A₂ cosφ. Step 2: Intensity is proportional to A²; constructive/destructive conditions are Δ = nλ and Δ = (n+½)λ. Step 3: Apply the stated phases/path differences. Final: A: 0, 1/3, 2/3, ….