Kundt's tube - AbsoluteAstronomy.com

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

August Kundt

August Adolf Eduard Eberhard Kundt was a German physicist.-Biography:Kundt was born at Schwerin in Mecklenburg. He began his scientific studies at Leipzig, but afterwards went to Berlin University. At first he devoted himself to astronomy, but coming under the influence of H. G...

for the measurement of the speed of sound

Speed of sound

The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....

in a gas

Gas

Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

or a solid

Solid

Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...

rod. It is used today only for demonstrating standing wave

Standing wave

In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling...

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

Cork (material)

Cork is an impermeable, buoyant material, a prime-subset of bark tissue that is harvested for commercial use primarily from Quercus suber , which is endemic to southwest Europe and northwest Africa...

dust, talc

Talc

Talc is a mineral composed of hydrated magnesium silicate with the chemical formula H2Mg34 or Mg3Si4O102. In loose form, it is the widely-used substance known as talcum powder. It occurs as foliated to fibrous masses, its crystals being so rare as to be almost unknown...

or Lycopodium

Lycopodium

Lycopodium is a genus of clubmosses, also known as ground pines or creeping cedar, in the family Lycopodiaceae, a family of fern-allies...

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

Pure tone

A pure tone is a tone with a sinusoidal waveshape.A sine wave is characterized by its frequency, the number of cycles per second—or its wavelength, the distance the waveform travels through its medium within a period—and the amplitude, the size of each cycle...

). Kundt used a metal rod resonator

Resonator

A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonant frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical...

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

Loudspeaker

A loudspeaker is an electroacoustic transducer that produces sound in response to an electrical audio signal input. Non-electrical loudspeakers were developed as accessories to telephone systems, but electronic amplification by vacuum tube made loudspeakers more generally useful...

attached to a signal generator

Signal generator

Signal generators, also known variously as function generators, RF and microwave signal generators, pitch generators, arbitrary waveform generators, digital pattern generators or frequency generators are electronic devices that generate repeating or non-repeating electronic signals...

producing a sine wave

Sine wave

The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...

. The other end of the tube is blocked by a moveable 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

In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...

, this means its length is a multiple of the wavelength

Wavelength

In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

of the sound wave. At this point the sound waves in the tube are in the form of standing wave

Standing wave

s, and the amplitude

Amplitude

Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

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

Node (physics)

A node is a point along a standing wave where the wave has minimal amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the...

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 wavelength

Wavelength

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 air:

The detailed motion of the powder is actually due to an effect called acoustic streaming
Acoustic streaming
Acoustic streaming is a steady current 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....

caused by the interaction of the sound wave with the boundary layer

Boundary layer

In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface where effects of viscosity of the fluid are considered in detail. In the Earth's atmosphere, the planetary boundary layer is the air layer near the ground affected by diurnal...

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

.Rosin, also called colophony or Greek pitch , 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 components. It is semi-transparent and varies in color from yellow to black...

, the rod vibrated longitudinally

Longitudinal wave

Longitudinal waves, as known as "l-waves", are waves that have the same direction of vibration as their direction of travel, which means that the movement of the medium is in the same direction as or the opposite direction to the motion of the wave. Mechanical longitudinal waves have been also...

at its fundamental frequency

Fundamental frequency

The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the lowest frequency of a periodic waveform. In terms of a superposition of sinusoids The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the...

, giving out a high note. Once the speed of sound in 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:

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 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

Further reading