Practice question

**Organ pipe modes** illustrate boundary influence. Closed pipe odd harmonic series contrasts with open pipe full series, affecting timbre. Frequency scales inversely with length, explaining pitch variation with pipe length. For closed pipe: v_n = (n + (1/2)) (v/2L) , n = 2 for third harmonic. v₂ = (2 + (1/2)) (360/2 × 0.8) = 2.5 × (360/1.6) = 2.5 × 225 = 562.5 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 562.5 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.