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 open pipe: v_n = (n v/2L) . Second harmonic ( n = 2 ): v₂ = (2 × 330/2 × 0.75) = (660/1.5) = 440 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 440 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.