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

speed of sound The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elasticity (solid mechanics), elastic medium. More simply, the speed of sound is how fast vibrations travel. At , the speed of sound in a ...

in a gas or a

solid Solid is a state of matter where molecules are closely packed and can not slide past each other. Solids resist compression, expansion, or external forces that would alter its shape, with the degree to which they are resisted dependent upon the ...

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 wave In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with respect t ...

s and acoustical forces.

How it works

The tube is a transparent 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 . Talc in powdered form, often combined with corn starch, is used as baby powder. This mineral is used as a thickening agent and lubricant ...

or lycopodium. At one end of the tube is a source of sound at a single frequency (a pure tone). 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 reso ...

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, more fully, a speaker system) is a combination of one or more speaker drivers, an enclosure, and electrical connections (possibly including a crossover network). The speaker driver is an ...

attached to a

signal generator A signal generator is one of a class of Electronics, 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, typ ...

producing a

sine wave A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic function, periodic wave whose waveform (shape) is the trigonometric function, trigonometric sine, sine function. In mechanics, as a linear motion over time, this is ''simple ...

. 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 is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...

. 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 and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...

''λ'' of the

sound wave In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...

s. 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

s, 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'' 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 Boundary (thermodynamic), bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces ...

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 known as colophony or Greek pitch (), is a resinous material obtained from pine trees and other plants, mostly conifers. The primary components of rosin are diterpenoids, i.e., C20 carboxylic acids. Rosin consists mainly of r ...

, the rod vibrated longitudinally at its

fundamental frequency The fundamental frequency, often referred to simply as the ''fundamental'' (abbreviated as 0 or 1 ), is defined as the lowest frequency of a Periodic signal, periodic waveform. In music, the fundamental is the musical pitch (music), pitch of a n ...

, 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