Practice question

**Superposition principle** states resultant displacement equals algebraic sum of individual waves, y = y₁ + y₂. For coherent waves with phase difference φ, resultant amplitude A = √(a₁² + a₂² + 2a₁a₂ cosφ), equal amplitudes give A = 2a cos(φ/2), constructive when φ = 2nπ, destructive when φ = (2n+1)π. For two identical waves with phase difference Φ = π , the resultant amplitude is A = 2a cos(Φ/2) = 2a cos(π/2) = 0 , leading to complete cancellation. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Becomes zero, illustrating frequency-length-speed interdependence and quantization by boundaries.