Kundt's tube is an experimental acoustical apparatus invented in 1866 by German physicist August Kundt for the measurement of the speed of sound in a

gas Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...

or a

solid Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structural ...

rod. The experiment is still taught today due to its ability to demonstrate longitudinal waves in a gas (which can often be difficult to visualise). It is used today only for demonstrating standing waves and acoustical forces.

How it works

The tube is a

transparent Transparency, transparence or transparent most often refer to: * Transparency (optics), the physical property of allowing the transmission of light through a material They may also refer to: Literal uses * Transparency (photography), a still, ...

horizontal pipe which contains a small amount of a fine powder such as cork dust,

talc Talc, or talcum, is a clay mineral, composed of hydrated magnesium silicate with the chemical formula Mg3Si4O10(OH)2. Talc in powdered form, often combined with corn starch, is used as baby powder. This mineral is used as a thickening agent a ...

lycopodium ''Lycopodium'' (from Greek ''lykos'', wolf and ''podion'', diminutive of ''pous'', foot) is a genus of clubmosses, also known as ground pines or creeping cedars, in the family Lycopodiaceae. Two very different circumscriptions of the genus are i ...

. At one end of the tube is a source of sound at a single frequency (a

pure tone Pure may refer to: Computing * A pure function * A pure virtual function * PureSystems, a family of computer systems introduced by IBM in 2012 * Pure Software, a company founded in 1991 by Reed Hastings to support the Purify tool * Pure-FTPd, ...

). Kundt used a metal rod

resonator A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator ...

that he caused to vibrate or 'ring' by rubbing it, but modern demonstrations usually use a

loudspeaker A loudspeaker (commonly referred to as a speaker or speaker driver) is an electroacoustic transducer that converts an electrical audio signal into a corresponding sound. A ''speaker system'', also often simply referred to as a "speaker" or ...

attached to a

signal generator A signal generator is one of a class of electronic devices that generates electrical signals with set properties of amplitude, frequency, and wave shape. These generated signals are used as a stimulus for electronic measurements, typically used i ...

producing a sine wave. The other end of the tube is blocked by a movable piston which can be used to adjust the length of the tube. The sound generator is turned on and the piston is adjusted until the sound from the tube suddenly gets much louder. This indicates that the tube is at

resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...

. This means the length of the round-trip path of the sound waves, from one end of the tube to the other and back again, is a multiple of the

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...

''λ'' of the sound waves. Therefore, the length of the tube is a multiple of half a wavelength. At this point, the sound waves in the tube are in the form of standing waves, and the

amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...

of vibrations of air is zero at equally spaced intervals along the tube, called the

node In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex). Node may refer to: In mathematics * Vertex (graph theory), a vertex in a mathematical graph *Vertex (geometry), a point where two or more curves, lines ...

s. The powder is caught up in the moving air and settles in little piles or lines at these nodes, because the air is still and quiet there. The distance between the piles is one half

''λ''/2 of the sound. By measuring the distance between the piles, the wavelength ''λ'' of the sound in air can be found. If the frequency ''f'' of the sound is known, multiplying it by the wavelength gives the speed of sound ''c'' in the air: :

c = \lambda f \,

The detailed motion of the powder is actually due to an effect called ''

acoustic streaming Acoustic streaming is a steady flow in a fluid driven by the absorption of high amplitude acoustic oscillations. This phenomenon can be observed near sound emitters, or in the standing waves within a Kundt's tube. Acoustic streaming was explaine ...

'' caused by the interaction of the sound wave with the

boundary layer In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary cond ...

of air at the surface of the tube.

Further experiments

By filling the tube with other gases besides air, and partially evacuating it with a vacuum pump, Kundt was also able to calculate the speed of sound in different gases at different pressures. To create his vibrations, Kundt stopped the other end of the tube with a loose-fitting stopper attached to the end of a metal rod projecting into the tube, clamped at its center. When it was rubbed lengthwise with a piece of leather coated with

rosin Rosin (), also called colophony or Greek pitch ( la, links=no, pix graeca), is a solid form of resin obtained from pines and some other plants, mostly conifers, produced by heating fresh liquid resin to vaporize the volatile liquid terpene comp ...

, the rod vibrated longitudinally at its

fundamental frequency The fundamental frequency, often referred to simply as the ''fundamental'', is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. I ...

, giving out a high note. Once the speed of sound in the air was known, this allowed Kundt to calculate the speed of sound in the metal of the resonator rod. The length of the rod ''L'' was equal to a half wavelength of the sound in metal, and the distance between the piles of powder ''d'' was equal to a half wavelength of the sound in air. So the ratio of the two was equal to the ratio of the speed of sound in the two materials: :

\frac  = \frac  = \frac  = \frac \,

Reason for accuracy

A less accurate method of determining wavelength with a tube, used before Kundt, is simply to measure the length of the tube at resonance, which is approximately equal to a multiple of a half wavelength. The problem with this method is that when a tube of air is driven by a sound source, its length at resonance is not exactly equal to a multiple of the half-wavelength. Because the air at the source end of the tube, next to the speaker's diaphragm, is vibrating, it is not exactly at a node (point of zero amplitude) of the standing wave. The node actually occurs some distance beyond the end of the tube. Kundt's method allowed the actual locations of the nodes to be determined with great accuracy.

How it works

Further experiments

Reason for accuracy

See also

References

Further reading