Concepts Of Physics MCQ Edition [Volume 1]PhysicsSound Waves
As shown in the figure, two coherent sources S₁ and S₂ emit sound of wavelength in phase. The separation between the sources is 3 . A circular wire of large radius is placed such that S₁ S₂ lies in its plane, with the middle point of S₁ S₂ located at the centre of the wire. Determine the angular positions in the first quadrant on the wire at which constructive interference takes place.
Options
- A0^ , ⁻¹ ( 1 3 ), ⁻¹ ( 2 3 ), 90^
- B0^ , 30^ , 45^ , 60^ , 90^
- C0^ , ⁻¹ ( 2 3 ), ⁻¹ ( 1 3 ), 90^
- D0^ , ⁻¹ ( 3 4 ), ⁻¹ ( 1 4 ), 90^
Correct answer
C. 0^ , ⁻¹ ( 2 3 ), ⁻¹ ( 1 3 ), 90^
Step-by-step solution
Let the distance between the two coherent sources S₁ and S₂ be d = 3 . For a point P on the circular wire of large radius at an angular position , the rays from S₁ and S₂ are approximately parallel. The path difference x between the waves reaching point P from S₁ and S₂ is given by: x = d Substituting d = 3 , we get: x = 3 For constructive interference, the path difference must be an integral multiple of the wavelength : x = n Equating the two expressions for path difference: 3 = n = n 3 Since we need the angular p