The pitch we hear is determined by the length of the that forms inside the tube.
Frequencies the cutoff are reflected back, keeping the note stable and clear.
The magnitude of this end correction depends heavily on the physical geometry of the hole:
Cylindrical pipes are mathematically simple, but most instruments (oboes, bassoons, saxophones) are conical—their bore expands linearly from mouthpiece to bell. A complete cone behaves like an open pipe of equivalent length, producing all harmonics. However, a truncated cone (like a saxophone) creates a unique impedance spectrum. Conical bores provide a richer, more blended set of partials and facilitate easier overblowing into the upper registers than a purely cylindrical closed pipe.
The proximity of a pad or key mechanism hovering over an open hole restricts airflow, artificially increasing the chimney depth and lowering the pitch. 4. Design Trade-Offs: Size, Placement, and Tone Quality