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. Fundamental: v₁ = (v/2L) . 120 = (48/2L) ⇒ 2L = (48/120) ⇒ 2L = 0.4 ⇒ L = 0.2 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 0.2 m, illustrating frequency-length-speed interdependence and quantization by boundaries.