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. Beats occur when two waves of slightly different frequencies superpose, causing constructive and destructive interference periodically, resulting in alternating loudness (waxing and waning). Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Beats, illustrating frequency-length-speed interdependence and quantization by boundaries.