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. Speed: v = √((T/μ)) = √((225/0.025)) = √(9000) ≈ 94.87 m/s . Wavelength: λ = (v/v) = (94.87/30) ≈ 3.16 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 3.16 m, illustrating frequency-length-speed interdependence and quantization by boundaries.