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. A small frequency difference produces a slow amplitude modulation (beat frequency = |f₁ - f₂| ), detectable by the human ear. Large differences result in rapid oscillations perceived as separate tones. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields To produce audible interference, illustrating frequency-length-speed interdependence and quantization by boundaries.