Air Column Resonance

The resonant frequencies of air columns depend upon the speed of sound in air as well as the length and geometry of the air column. Longitudinal pressure waves reflect from either closed or open ends to set up standing wave patterns. Important in the visualization of these standing waves is the location of the nodes and antinodes of pressure and displacement for the air in the columns.

For temperature T= C the speed of sound is m/s.

Open cylinder

Closed cylinder

Closed cone
Length L=m
Length L=m
Length L=m
Hz
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Any of the values may be changed. The calculation defaults to a 1 meter open column at temperature 20 C if data for length and temperature are not entered.
Application in musical instruments
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Open Cylinder Air Column

A cylindrical air column with both ends open will vibrate with a fundamental mode such that the air column length is one half the wavelength of the sound wave. Each end of the column must be an antinode for the air

motion since the ends are open to the atmosphere and cannot produce significant pressure changes. For the fundamental mode, there is one node at the center. The basic wave relationship leads to the frequency of the fundamental:

The open air column can produce all harmonics. Open cylinders are employed musically in the flute, the recorder, and the open organ pipe.

CalculationComparison of air columnsRijke tube resonator
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Harmonics of Open Air Column

An open cylindrical air column can produce all harmonics of the fundamental. The positions of the nodes and antinodes are reversed compared to those of a vibrating string, but both systems can produce all harmonics. The sinusoidal patterns indicate the displacement nodes and antinodes for the harmonics. A pressure node corresponds to a displacement antinode, and the harmonic patterns can also be visualized in terms of air pressure or density patterns.
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Air Column Standing Waves

This is a depiction of air pressure and density variations for first five standing wave modes of an open cylinder. The ends are constrained to be nodes of pressure, being essentially at atmospheric pressure. A half cycle later, all the high pressure points would be low pressure points, and vice versa.

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