Two coherent waves have maximum and minimum resultant intensities satisfying Iₘₐₓ/Iₘᵢₙ = 9. If the larger individual intensity is N times the smaller individual intensity, find N.
Physics · Wave Motion · Reflection, Refraction and Superposition of Waves
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Question

Two coherent waves have maximum and minimum resultant intensities satisfying Iₘₐₓ/Iₘᵢₙ = 9. If the larger individual intensity is N times the smaller individual intensity, find N.

G1 Physics · Accepted Answer

Let the larger and smaller wave amplitudes be a₁ and a₂, with a₁ > a₂. Then, Iₘₐₓ/Iₘᵢₙ = [(a₁+a₂)/(a₁−a₂)]². Given, [(a₁+a₂)/(a₁−a₂)]² = 9. Taking the positive square root, (a₁+a₂)/(a₁−a₂) = 3. Thus, a₁+a₂ = 3a₁−3a₂. Therefore, 2a₁ = 4a₂, so a₁/a₂ = 2. Intensity is proportional to amplitude squared. Hence, I₁/I₂ = (a₁/a₂)² = 4. Therefore, N = 4.