Practice question

**Superposition of nearly equal frequencies** creates resultant y = 2A cos(Δω·t/2) sin(ω_avg·t), envelope frequency Δf/2, beat frequency Δf. Total beats heard in Δt is f_beat·Δt, explaining counting over seconds. For constructive interference with equal amplitudes a , the resultant amplitude is 2a . Intensity is proportional to the square of amplitude, so I ∝ (2a)² = 4a² , quadrupling the individual intensity. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields It quadruples, illustrating frequency-length-speed interdependence and quantization by boundaries.