Like strings or springs, air or gas contained within a tube can vibrate with sound frequencies. This is the principle that constitutes musical instruments such as the flute, horn, clarinet, etc. which are basically built by sound tubes.
In these instruments, a column of air is vibrated by blowing one end of the tube, called the nozzle, which has the appropriate vibrating devices.
The tubes are classified as open and closed, the open tubes being those with both ends open (one near the mouth) and the closed tubes having one open end (near the mouth) and the other closed.
The vibrations of the gas columns can be studied as standing waves resulting from the interference of the sound sent in the mouth with the sound reflected in the other end of the tube.
At an open end the sound is reflected in phase, forming a womb (constructive interference) and at a closed end occurs phase inversion reflection, forming a displacement knot (destructive interference).
Considering a long sound tube ℓwhose waves propagate at a speed v.
Thus the possible standing wave configurations are:
Ways to vibrate can, from these examples, be generalized as:
And the frequency of harmonics will be given by:
How no there are no restrictions, in the open tube natural frequencies of all harmonics are obtained.