Leonardo

Art on a Two-Dimensional Flame TableAuthor(s): Harold A. DawReviewed work(s):Source: Leonardo, Vol. 24, No. 1 (1991), pp. 63-65Published by: The MIT PressStable URL: http://www.jstor.org/stable/1575470 .Accessed: 11/06/2012 18:42

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TECHNICAL NOTE

Art on a

Two-Dimensional Flame Table

Harold A. Daw

P hysics has an intrinsic beauty. The beauty is found in the symmetry of its laws (often evident only to those who understand the mathematics used to describe the laws), in the clean lines of much of its apparatus, and in the

phenomena with which it deals. Often there arises some- thing related to art.

This paper describes a modest contribution to kinetic art from the field of acoustics, a branch of physics dealing with sound. In this work the normal mode structure of standing waves in an acoustic cavity was made visible by means of gas flames on a two-dimensional flame table, which is related to other devices used to make standing wave patterns visible. The flame table is related to Kundt's tubes [1] and more

closely to the Rubens flame tube [2], both one-dimensional demonstrations. The Rubens flame tube has received some attention [3,4]. In two dimensions, experiments with stand- ing waves on Chladni plates [5] are a close relative.

The flame tables, developed in the Physics Department at New Mexico State University, are described in this paper, and several photographs of normal modes of sound waves

Fig. 1. The two-dimensional flame tables. The tables have hollow metal cavities into which gas is introduced. The gas comes out through the many small holes on the top surfaces and is lighted. Pure sound frequencies excite the resonant sound modes of the cavities, causing flame patterns unique to the particular table shape and resonant mode.

PHENOLIC TUBE DRIVER

are presented. In some ways this paper is related to an ear- lier publication on ultrasound images [6].

It has been pointed out that the work described here is re- lated to an earlier work by Gyorgy Kepes called Flame Or- chard [7]. Since Flame Orchard either no longer exists, or is in Medellin, Columbia, I have not been able to see it. Kepes'swork is described in an article byjasia Reichardt [8] (she calls the work Fire Orchard). The article contains a picture of the flames, and if the table width was 2 ft as indicated in the text, the hole spacing would have been 4 inches on the original table.

A flame table patterned

ABSTRACT

The author describes a new device for viewing the normal mode patterns of sound waves in a cavity. This device uses gas flames to make the modes visible. Viewers experience both the sound frequen- cies from an audio oscillator used to excite the acoustic cavity, and the gas flame patterns that reveal the mode patterns for the sound waves.

somewhat after the original Flame Orchard is currently under construction by Paul Earls, current director of the MIT Center for Advanced Visual Studies. It has holes about 1/8 inch in diameter on about a 4-inch grid. Again, this size grid lacks the resolution needed on a 2-ft-square table to display the modes. Nevertheless, it has features in common with the subject of this paper.

THE APPARATUS

I observed the normal mode structure on a device called a two-dimensional flame table. I made three different types of flame tables: one shaped like a shallow square box, another like a shallow cylinder and a third like an equilateral tri- angle. Diagrams of the three tables are shown in Fig. 1. Two of the devices are described in detail in a physics publication [9].

Except for a speaker mount and a gas port, each flame table is closed on all sides. The flame tables, which are about 2 ft across in the major direction and 4 in deep, are made of 1/8-in-thick aluminum sheet. The tops of the square and circular tables are perforated with about 400 holes that are .040 inch in diameter (#60 drill) on a 1-in-square grid. In the case of the triangular table, the holes are .028 inch in diameter (#70 drill) on a .66-in grid. Each table is supported

Harold A. Daw (educator, physicist), Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003, U.S.A.

Received 25 May 1989.

? 1991 ISAST Pergamon Press plc. Printed in Great Britain. 0024094X/91 $3.00+0.00 LEONARDO, Vol. 24, No. 1, pp. 63-65, 1991 63

I

Fig. 2. Flame pattern on the surface of the square table. This pat- tern was produced when a sound frequency of 820 cps was intro- duced to the flame table cavity. This pattern corresponds to m = 2 and n = 2 in cos(7rmx/L) cos(Qtny/L).

by legs to keep it away from other sur- faces because it becomes quite hot. A port for admitting gas into the hollow cavity of the table is provided in the side of each table. The port accepts a 1/4-in hose. A second port is provided in the side of each table for a loudspeaker driver. This hole, 1.361 inches in dia- meter with 18 threads per inch, accepts a standard speaker driver. The driver is mounted on a 2-in phenolic spacer to prevent heat conduction to the speaker.

Gas is admitted into the cavity via a pressure regulator and ignited as it comes out of the 400 holes. With the gas burning at each of the holes, the table resembles a birthday cake (round, square, or triangular) with 400 very short candles. Methane gas and liquid petroleum gas (LPG) work well. The LPG produces more colorful flames, is more spectacular to view and is easier to photograph.

A word of caution relative to the heat generated by the table: the table gets hot enough to burn and should only be touched with care. Caution should also be used in igniting the gas. LPG is heavier than air and will settle down the sides of the table rather than rise. Thus, LPG should be ignited by placing the match to the edge of the table rather

Fig. 3. Flame pattern on the surface of the circular table. This pat- tern was produced when a sound frequency of 1120 cps was intro- duced to the flame table cavity. This pattern corresponds to n = 0 inJ(w r/v) cos(nO).

than above it. Methane rises and may be lit above the table.

When the gas is lit, the internal cavity is acoustically excited using a regular audio speaker driver [10]. An audio frequency generator is used for the sound source along with an audio am- plifier [ 11 ]. As the driving frequency is changed, the flames on the surface respond dramatically, displaying the structure of the standing sound wave pattern in the cavity. The most visually interesting patterns occur at acoustic resonances of the cavity. As the fre- quency of the audio frequency gener- ator is changed, the sound level changes. As a resonance is approached, the sound level increases and the flames move like soldiers to display the resonant mode shape.

HOW THE FLAME PATF ERNS ARE FORMED

I will not discuss the details of the theory of the flame pattern formation here; they are covered elsewhere [12]. Suffice it to say that the patterns on the square table are described by sinusoidal functions, those on the circular table by Bessel and sinusoidal functions, and those on the triangular table by more

complicated functions. The result is that the flames are strongest where the pressure amplitude is least. The flames form at what are called the pressure nodes of the cavity. Only a few of the standing wave patterns can be shown in this paper. The general features, how- ever, can be described. The patterns on the square table follow patterns given by zeros in the function

cos (gmx/L) cos (rcny/L)

where L is the length of the table, x and y are distances along the table, and m and n are integers. The results are ladder- like structures with flame lines parallel to the table edges. Up to 3 node lines (positions where equation 1 is zero) were photographed in each direction. This would correspond to m = n = 3. All lower values of m and n have been photographed.

The patterns on the circular table are given by an equation of the form

Jn (o( r/v) cos (nO)

where Jn is a Bessel function, Co is the radian sound frequency, r is the radial distance on the table, v is the speed of sound in the gas, 0 is the angular position on the table, and n is an in- teger. The patterns in this case look like

64 Daw, Art on a Two-Dimensional Flame Table

stars and circles and combinations of the two.

The patterns on the triangular table are more complicated to describe. The lowest mode is one in which there are flames in the center of the table and toward each of the end points, but not at the end points. The other shapes are more complicated but have a triangular symmetry.

Photographs of several flame pat- terns are presented in Figs 2-4 and in Color Plate A No. 1. The proper camera

setting will vary considerably because the patterns are affected by a number of factors. I have had success with film of speed ISO 400, F# 5.6 at a shutter

speed of 1/60 sec. The resonant frequencies fall in the

range of 500-1,500 cycles per second

(cps) for LPG. When methane is used, the frequencies are all higher by about 50%.

PHOTOGRAPHING THE FLAME PATTERNS

A number of variables beyond those

normally associated with taking a pic- ture have to be considered to produce good flame table photographs. The sound intensity level as well as the gas pressure influences good patterns. The

pressure level will affect the amount of

light produced. Also, the type of gas will have considerable influence since methane produces less light than LPG. As the amount of gas in the flame is

changed, the temperature of the table and hence the speed of the sound in the

gas will be affected. This will cause a drift in the pattern. But a change in the flow rate of the gas will change the gas pressure if a bottle of LPG is being used, and this requires an adjustment of the flow regulator. Drift in the audio

frequency generator is a minor prob- lem, but some other effects require ad-

justing the frequency to get a good pat- tern. It is helpful to have one person operate the camera while another per- son adjusts the gas level and sound

frequency for the best patterns. One can be sure of obtaining good photo- graphs if the exposure is right and the other adjustments produce a good visual pattern.

SPECULATIONS

I have dealt with only three cavity shapes: square, round and triangular.

Fig. 4. Flame pattern on the surface of the triangular table. This pattern was produced when a sound frequency of 1110 cps was introduced to the flame table cavity.

But what would the flame structure be for other cavity shapes? One can easily visualize the modes on an elliptical or oval cavity, but what of more exotic

shapes, for example, a violin shape? Also, our research only dealt with single frequency input; more complicated patterns would result if resonant fre-

quencies were mixed. If the cavity depth were increased, modes with a vertical standing wave component could be seen. Finally, putting metal salts into the gas would change the color of the flames.

References and Notes

1. H. Meiners, Physics Demonstration Experiments, Vol. 1 (Ronald: New York, 1970) p. 493.

2. H. Rubens and 0. Krigar-Menzel, "Flammen- rohre fur akustische Beobachtungen", Annalen der Physik 17 (1905) p. 149.

3. G. Ficken and F. C. Stephenson, "Rubens Flame Tube Demonstration", ThePhysics Teacherl 17 (1979) p. 306.

4. G. F.Spagna, Jr., "Rubens Flame Tube Demon- stration: A Closer Look at the Flames", TheAmerican Journal of Physics 51 (1983) p. 848.

5. H. C.Jensen, "Production of Chladni Figures on Vibrating Plates Using Continuous Excitation", The American Journal of Physics 23 (1955) p. 503.

6. P. Gregus, "A New Medium for Visual Artists: Ultrasonic Imaging", Leonardo 16, No.1 (1983) p. 38.

7. Gyorgy Kepes, The MIT Years: 1945-1977 (Cam- bridge, MA: MIT Press, 1978) p. 67. Kepes was the director of the MIT Center for Advanced Visual Studies and is presently its emeritus director.

8. Jasia Reichardt, "Art at Large", New Scientist 54 (1972) p. 525.

9. Harold A. Daw, "A Two-Dimensional Flame Table", The American Journal of Physics 55 (1987)

p. 733.

10. The audio speaker driver used was a PD-60 T Atlas Sound.

11. The audio frequency generator used was a Hewlett-Packard 200 AB. The audio amplifier was a Scott 250 BRL.

12. Harold A. Daw, 'The Normal Mode Structure on the Two-Dimensional Flame Table", The Ameri- can Journal of Physics 56 (1988) p. 913.

Daw, Art on a Two-Dimensional Flame Table 65