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. Fundamental: v₁ = (v/2L) . 510 = (340/2L) ⇒ 2L = (340/510) ⇒ 2L = (2/3) ⇒ L = 0.333 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 0.33 m, illustrating frequency-length-speed interdependence and quantization by boundaries.