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. The beat frequency, |f₁ - f₂| , is the rate at which amplitude modulates, perceived as periodic loudness variations, equal to the difference in wave frequencies. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Difference in frequencies, illustrating frequency-length-speed interdependence and quantization by boundaries.