Kundt's dust pipe

Representation of the apparatus and the dust figures
from the original work of August Kundt, 1866

The Kundt tube (also Kundt tube ; after the physicist August Kundt , of his observations published in 1866) allows standing acoustic waves to make visible in a glass tube. Standing waves result in z. B. The tone of almost all musical instruments , especially all types of flutes and pipes . Due to its simple and clear structure, the Kundt pipe is a popular demonstration experiment in school physics .

construction

Schematic representation of Kundt's tube with sound velocity distribution. The cork flour collects at the nodes of the standing wave

The cork powder contained in the pipe is moved by the intense sound wave. It collects in places where the sound velocity of the sound waves is smallest, i.e. H. into the knot of the standing wave, where it forms small heaps of flour. Consequently, the antinodes of the standing wave are located between these piles of flour.

The piles of flour are retained even after switching off the Sinustone . They are not to be confused with “setting up” the cork flour with the sine tone switched on (at medium amplitudes or loudnesses of the sine tone, the cork flour rises at the antinodes and remains almost immobile in a mostly lamellar structure. At higher amplitudes, these lamellar elevations are not to see that the cork flour is swirled up too much).

So that resonance - d. H. a standing wave  - occurs, the length of the pipe must be adjusted by a punch that can be pushed into the pipe from one side. At the punch there is a closed end (and therefore a vibration node), while at the open end of the pipe there is an antinode. Bear moss spores may look better than cork flour because they are smaller and lighter.

Physical basics

In order to deduce when a standing wave occurs in Kundt's tube, the fast wave of the sound is considered. One end of the air-filled glass tube is closed by a stamp, the other end is open. In front of the open end is the sound source , a very powerful loudspeaker .

• At the open end, the fast has a wave belly, i. H. maximum deflection because the open end resonates; the incoming sound waves vibrate in unison with the membrane of the speaker .
• On the other hand, there must be a fast wave node at the closed, fixed end because the end is rigid and therefore does not oscillate.

As a result of these prerequisites, for a given wavelength there are only certain pipe lengths in question, at which resonance occurs: The length of the pipe must be a multiple of half the wavelength minus a quarter wavelength : ${\displaystyle \lambda }$ ${\displaystyle l}$ ${\displaystyle \lambda /2}$ ${\displaystyle \lambda /4}$

${\displaystyle {\begin{aligned}l&=k\cdot {\frac {\lambda _{k}}{2}}-{\frac {\lambda _{k}}{4}},\quad \quad k\in \mathbb {N} \\&=(2k-1)\cdot {\frac {\lambda _{k}}{4}}\end{aligned}}}$

Substituting with the speed of sound and resolving for the resonance frequency results in: ${\displaystyle \lambda _{k}={\frac {c}{f_{k}}}}$ ${\displaystyle c}$ ${\displaystyle f_{k}}$

${\displaystyle \Rightarrow f_{k}=(2k-1)\cdot {\frac {c}{4l}}}$

There is resonance for the vibrations . The frequency is called fundamental or first harmonic, the other frequencies for the first  harmonic or second harmonic, the second harmonic or third harmonic, etc. ${\displaystyle f_{k}}$ ${\displaystyle f_{1}}$ ${\displaystyle k>1}$

Measurement of the speed of sound in air

Practical construction of a Kundt dust tube

See also : "Measuring the wave impedance" in the article Wave impedance

Since sound waves can be made visible with the aid of Kundt's tube, the speed of sound can be measured with it. The previous equation gives:

${\displaystyle \Leftrightarrow c={\frac {f\cdot 4l_{k}}{2k-1}}}$

In the equation has been replaced by and through , since the length of the pipe is varied at a constant frequency when measuring the speed of sound . ${\displaystyle f_{k}}$ ${\displaystyle f}$ ${\displaystyle l}$ ${\displaystyle l_{k}}$ ${\displaystyle l}$

${\displaystyle k}$can be determined by counting the wave crests. However, since these may not be easy to see, a computational approach is recommended. To do this, the equation for two successive resonances at the same frequency must be equated:

${\displaystyle {\frac {f\cdot 4l_{k}}{2k-1}}={\frac {f\cdot 4{l_{k+1}}}{2k+1}}}$

${\displaystyle \Leftrightarrow k={\frac {l_{k+1}+l_{k}}{2\left(l_{k+1}-l_{k}\right)}}}$

${\displaystyle k}$can therefore be determined by measuring from and . Inserting and the given frequency in the above equation finally yields the speed of sound. ${\displaystyle l_{k}}$ ${\displaystyle l_{k+1}}$ ${\displaystyle k}$ ${\displaystyle f}$

literature

• Gottfried Schubert: Dust figures in Kundt's pipe . In: Physics in Our Time . tape 12 , no. 5 , 1981, pp. 147–150 , doi : 10.1002 / piuz.19810120503 .
• A. Kundt: About a new kind of acoustic dust figures and about their application to determine the speed of sound in solid bodies and gases . In: Annals of Physics and Chemistry , 1866, Volume 127, No. 4, pp. 497-523 on Google Books

Web links

Commons : Kundtsches Staubrohr  - Collection of images, videos and audio files

• Kundt's pipe . 2004 (video from the FH Kaiserslautern).

Individual evidence

1. ↑ August Kundt: About a new kind of acoustic dust figures and about the application of the same to determine the speed of sound in solid bodies and gases . In: Annals of Physics and Chemistry . tape 203 , no. 4 , 1866, pp. 497-523 , doi : 10.1002 / andp.18662030402 .