Practice question

**Beats arise** when two waves of slightly different frequencies f₁ and f₂ superpose, producing amplitude modulation at beat frequency f_beat = |f₁ - f₂| (Hz). Intensity waxes and wanes periodically, number of beats in interval Δt equals f_beat·Δt, loudness variation audible when f_beat < 10 Hz. Beat frequency: vbₑₐt = 480 - 475 = 5 Hz . Beats in 20 s: 5 × 20 = 100 . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 100, illustrating frequency-length-speed interdependence and quantization by boundaries.