Conical bore

A conical bore is an air column whose internal diameter widens along its length. It shapes an instrument’s resonances and radiation, often producing a tone resembling that of a cylindrical tube with a longer effective length.

Acoustic impedance: The frequency-dependent opposition a system presents to sound-wave flow. The bore’s changing cross-section alters the impedance seen by sound waves.
Cylindrical bore: An air column whose internal diameter remains approximately constant along its length. Its resonances differ from a cone’s, especially for instruments with an open end.
Oboe: A double-reed woodwind instrument with a narrow conical bore and a penetrating tone. Its conical bore helps produce a strongly harmonic spectrum and distinctive register behavior.
Clarinet: A single-reed woodwind instrument with a predominantly cylindrical bore and a characteristic low-register resonance pattern. Its cylindrical bore and closed-like mouthpiece end contrast with conical reed instruments.
Standing wave: A wave pattern formed when oppositely traveling waves interfere, producing fixed nodes and antinodes. Reflections in a conical air column establish standing-wave resonances.
Conical frustum: A cone with its tip cut off by a plane parallel to its base. Many instrument bores approximate a frustum rather than extending to a sharp apex.
Bassoon: A low-pitched double-reed woodwind instrument with a long, folded conical bore. Its folded cone makes a long resonating air column practical in a compact instrument.
Trumpet: A brass instrument with mostly cylindrical tubing that expands through a flared bell. Its largely cylindrical tube contrasts with brass instruments designed with more conical tubing.
Harmonic series: A sequence of frequencies that are integer multiples of a fundamental frequency. An ideal cone supports resonances close to integer-multiple harmonics.
Open pipe: A tube acoustically open at both ends, with pressure nodes near its openings. An ideal conical bore is often analyzed as an open pipe with a virtual apex.

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