Practice question

**Air column vibrations** depend on end conditions. Pipe closed at one end has displacement node at closed end and antinode at open, allowing only odd harmonics, fundamental f₁ = v/(4L). Open pipe has antinodes at both ends, fₙ = n·v/(2L), all harmonics present, v sound speed. For open pipe: v_n = (n v/2L) . Second harmonic ( n = 2 ): v₂ = (2 × 330/2 × 0.3) = (660/0.6) = 1100 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1100 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.