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. v_n = (n v/2L) . 637.5 = (n × 340/2 × 0.8) = (n × 340/1.6) . 637.5 = n × 212.5 ⇒ n = (637.5/212.5) = 3 . Third harmonic. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 3, illustrating frequency-length-speed interdependence and quantization by boundaries.