The reed/mouthpiece end behaves acoustically like a closed end (a pressure antinode — air can't easily escape there), while the bell and any open tone hole behave like an open end (a pressure node). The first open hole encountered travelling from the mouthpiece dominates: it vents the bore there, so the column that actually resonates is only as long as the distance to that hole — this is the standard "first open hole" cutoff approximation used in musical acoustics. Closing every hole lets the wave travel the full bore to the bell.
Bore shape changes which harmonics are allowed. A cylindrical bore closed at one end and open at the other (like a clarinet) only supports odd harmonics: fn = (2n−1)·c/(4·Leff) — this is why clarinets overblow a twelfth. A conical bore (like an oboe or saxophone) closed at its narrow apex still behaves like a fully open pipe of the same length once you solve the horn equation for a cone, so it supports every harmonic: fn = n·c/(2·Leff) — conical instruments overblow an octave.
- Cylindrical bore — constant cross-section (clarinet family): odd harmonics only.
- Conical bore — linearly flaring cross-section (oboe/saxophone family): all harmonics.
- Tone hole — opening it moves the effective open end from the bell to the hole, shortening Leff and raising the pitch.
This is the flat 2D companion to the 3D wind-instrument-acoustics simulation: the same bore/tone-hole resonance physics, viewed as a cross-section along the instrument's axis with the standing pressure wave drawn above the tube.