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. A pipe closed at one end has frequencies v_n = (2n - 1) (v/4L) , producing only odd harmonics (1, 3, 5, ..). A pipe open at both ends has all harmonics (1, 2, 3, ..), so even harmonics are absent in the closed pipe. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as