BESIDES BRINGING GOOD MUSIC TO the home, the high-fidelity reproduction of sound has introduced some devotees to a new hobby. In installing a hi-fi system, you must adjust and tinker to bring the system to its best performance, and during this process it is easy to develop an interest in the machinery as well as the music it reproduces. In the course of adjusting the tone controls, finding the best location in the room for the speaker, damping the speaker with rock wool, modifying the amplifiers, regulating the needle pressure, looking into volume expanders and so on, you are likely to discover the fascinating science of acoustics. Pursuing this further, you may find that you can use your sound system as an acoustic telescope, a microscope, a kind of X-ray machine and a general utility instrument.

A sound system does not have to be particularly "hi-fi" to serve for investigating the sound a fly makes when it walks upside down. You need a fairly sensitive system, however, to hear termites munching inside a wooden beam. Only the best equipment, carefully groomed for the job, will enable you to hear the so-called "dawn chorus," the mysterious "tweeks," "bonks" and "swishes" that appear to come from the ionosphere at sunrise [see article on page 34].

Many aspects of sound can be studied without any amplifying system at all. A simple apparatus built from common materials will serve to measure the speed of sound, study the pure tones that make up complex sounds, observe harmonic vibrations and perform many other experiments in what, until recently, was a long-neglected branch of science.

It seems strange that acoustics has long played the role of Cinderella among the physical sciences. Many people who know a good deal about the work of the pioneers in optics, mechanics, heat, electricity, magnetism and nuclear physics cannot even name their counterparts in acoustics. Yet the science has had a number of gifted workers. As a matter of fact the wave nature of sound was explained long before an equally solid theoretical footing was established for the study optics.

The first important name in acoustics was Marcus Vitruvius Pollio-who is also revered by architects. In his remarkable treatise De architectura, which appeared during the reign of the Roman emperor Augustus Caesar, Vitruvius wrote: "Now the sound of the voice is transmitted by a progressive motion in the air which can be perceived by the sense of hearing. It is propagated in the form of a countless series of concentric circles, as when a stone is thrown into standing water. Innumerable circular waves form and grow as they recede from the center of the disturbance until they reach some obstruction. When opposed, the first waves recoil and interfere with succeeding waves." After discoursing upon reverberation and wave interference, Vitruvius concluded: "Accordingly, the ancient architects constructed tiers of steps in theatres in harmony with clues they found by studying the facts about the voice."

After Vitruvius the study of facts about acoustics was pursued only spasmodically over the centuries. It has begun to come into its own only during the past quarter century, with the advent of electronics and especially under the stimulus of World War II. Today acoustical research is being applied in such fields as architecture, sound reinforcement, noise abatement and ultrasonics, which is rapidly making a place for itself in industry.

A hi-fi addict who wishes to explore the scientific aspects of sound can make a good start with the classic Chladni plate, invented by the 18th-century German physicist Ernst Chladni to study the nature of harmonic vibrations. Chladni's plate behaves much like the paper cone in a loud-speaker. Here is his account of the apparatus:

"As an amateur in music, the rudiments of which I had begun to study at the rather late age of 19, I noted that the theory of sound was more neglected than several other branches of physics. In 1785 I had observed that a plate of glass or metal, if clamped at the center, gave different sounds when struck at different places. But I found nowhere any account of these different modes of vibration. The journals had given at that time some notices about a musical instrument made in Italy by Abbé Mazzcchi, consisting of bells to which he applied violin bows. When I applied a bow to a round plate of brass fixed at its center, it emitted different tones, but the nature of the motions to which these sounds corresponded was still unknown to me. The experiments on electric figures that form on a resin plate dusted with powder led me to surmise that the different vibratory motions of a sonorous plate might also present a different appearance if I sprinkled on the surface a little sand.

"Upon applying this device, the first figure that presented itself to my eyes on the round plate resembled a star with 12 points. Just imagine my astonishment and delight upon beholding this sight which no one had ever seen before!"

A version of Chladni's plate is shown in the drawing above. It is made of hard aluminum sheet, but any good "bell" material will work. An old violin bow will spare you the labor of making the one shown. You sprinkle a layer of white sand evenly on the plate and then draw the bow over the edge. The sand grains collect in bands in the zones of least motion, and you can see the whole vibrating system. It is interesting to experiment with plates of various shapes: square, triangular, elliptical and so on. The edge of the plate should be free of grease, and the bowing action will be improved if you rub the strings with rosin. While bowing one point on the edge, touch your finger lightly to other points. You will get various interesting sand patterns, each corresponding to a different arrangement of standing waves in the plate and to a different tone.

The cone of a loud-speaker will show similar patterns if you coat it with a thin layer of powdered sulfur, lycopodium or similar material, using a small camel's hair brush to apply the powder. The ideal speaker cone would vibrate as a whole at every frequency instead of separating into zones, but paper cones rarely approach the ideal. As the frequency increases, movement is confined more and more to the central portion of the cone, although rays of vibration occasionally extend to the edge. The pattern depends on the thickness and composition of the material and the method of suspension at the center and the edge. Hi-fi students who make this experiment may be astonished to learn that many speakers assumed to have an effective diameter of 12 or 15 inches do a lot of their work within an acoustical diameter of less than three inches, with the remaining zones performing a bewildering series of gyrations which have little to do with the "facts of the voice."

Another simple and beautiful experiment, devised in 1876 by August Kundt of Germany, measures the velocity of sound. Kundt used a common wooden whistle as his source of sound, but in a modern laboratory version of his apparatus a vibrating steel rod is substituted for the whistle. The apparatus is illustrated on the left. The glass tube shown is a 40-watt fluorescent lamp with its ends cut off. (In cleaning out the tube be careful not to breathe in any of the material that comes out, because the phosphors and gas used in some of these lamps are poisonous.) You place inside the tube a small amount of lycopodium powder, powdered cork or precipitated silica, which will serve as the vibration indicator. One end of the tube is stopped with a movable piston, which will regulate the tube length. You cover the other end with a thin, stretched rubber or cellophane diaphragm, and against this diaphragm, making light contact with it, you place the end of a steel rod. The rod is supported and clamped at its mid-point as shown.

Now you stroke the outer end of the rod with a rosined chamois, making it vibrate. With a little practice you can make the rod "sing" in a strong monotone. The vibration of the rod against the diaphragm causes the powder inside the glass tube to fly around. You slowly move the piston at the other end of the tube until the length of the air column in the tube is tuned to "resonance" with the rod tone; that is, until standing waves are formed in the tube. You will recognize this event by a sudden increase in loudness of the sound. Now the flying powder inside the tube will settle and collect in little piles at "nodal" points where the air is not vibrating. There will be one node at the piston, one near the diaphragm and perhaps others between. The distance from one node to the next is half the wavelength of the sound tone, and so you can measure the wavelength with a ruler.

The wavelength times the frequency of the wave gives the velocity of the sound in the tube. To determine the velocity, therefore,

you need to know the frequency. You could arrange this simply by feeding a tone of known frequency into the tube, using, instead of a steel rod, a small horn [see lower part of illustration] hooked to a recording of a pure tone-the Westminster DRB hi-fi demonstration record is a good one for the purpose. But you can measure the frequency of the steel-rod vibrations yourself by matching it with a homemade siren. Take a 10-inch disk, perforate a series of quarter-inch holes around it near its rim at regularly spaced intervals, spin the disk with a direct-current motor and blow at the spinning holes with a soda straw. Each passage of air through a hole is a sound-making vibration, and blowing through the succession of holes will produce a typical siren tone, whose frequency is measured by the number of revolutions of the disk per second multiplied by the number of holes. Now you adjust the speed of the motor until the siren tone matches the tone from your steel rod in the Kundt apparatus. The calculation just described (assisted by a revolution counter to measure the speed of the motor) gives you the frequency of this tone.

With the Kundt tube you can measure the velocity of sound in gases other than air. If the gas in the tube is carbon dioxide, the nodes will fall closer together; in other words, in this gas a tone of a given frequency produces vibrations of shorter wavelength. This means that the; velocity of sound in carbon dioxide is less than in air. In hydrogen, on the other hand, sound will travel faster than in air.

You can also measure the speed of sound in the steel rod. The distance from the point at which the rod is clamped (not vibrating) to the end of the rod (where it vibrates most strongly) is half the distance between nodes, or one quarter of a wavelength. The ratio between the wavelength of sound in the rod to its wavelength in the air of the tube measures the ratio of the speed of sound in steel to the speed in air. Consequently, having determined the wavelength in the tube, you can easily calculate the velocity of sound in the rod.

The fact that the speed of sound varies with the material through which it travels implies that a beam of sound waves will be refracted when passing from one material to another. It should be possible, therefore, to make "lenses or "prisms" which will have the same effect on sound as a glass lens has on light. Physicists at the Bell Telephone Laboratories have designed various such devices. One of them is illustrated above. The lens consists of carbon dioxide gas in a lens-shaped volume enclosed by two rubber diaphragms. The dimensions are not critical. Care should be taken to make a tight joint at the edge of the rubber sheeting and at the point where the inlet tube enters the lens. It helps if you are generous with rubber cement The so-called "rubber dam" sheeting carried by dealers in dental supplies is convenient to use and works well.

As in optics, the dimensions of an acoustic lens must be substantially greater than the wavelength of the sound if it is to bend the waves into sharp focus. For long sound waves in the lower range of hearing the lens would have to be much too large. But a fairly high-pitched sound such as one of 8,600 cycles per second, whose waves are about an inch and a half long, can be focused to a sharp "image" with a gas lens 12 inches in diameter inflated with carbon dioxide to a thickness of five inches. You can pick up the "image" with a stethoscope.

An acoustical lens of this type has one great advantage over its optical counterparts: its focal length can be varied simply by inflating or deflating it. Indeed, you can even focus sound rays with a toy balloon. Blow up a balloon (preferably with carbon dioxide) and put your ear close to one side while holding your wrist watch close to the other. The ticks will come through much louder than you can hear them with the unaided ear.

A more useful form of the acoustical lens is shown in the drawing below. Here a barrier of slats refracts the sound waves, in effect, by increasing the length of their path to the place where they are heard. The amount of refraction varies directly with the width of the slats and inversely with the spacing between them. The structure must be large in proportion to the wavelength and the spacing of the slats small. The lens illustrated here is of the dispersing or "negative" type: it is designed to spread the beam of a loud-speaker into the fan-shaped pattern desired for good listening in all parts of a living room. Its two-inch spacing limits this lens to frequencies below 8,000 cycles; for higher frequencies the spacing must be reduced and more slats added.

You do not need lenses to take up acoustic microscopy. A microphone which is not too noisy will pick up sounds far below the threshold of human hearing. You simply hook it to the input circuit of the sound system where the phone pickup is normally connected, and turn up the volume for as much acoustic magnification as you need. In making these experiments, be careful not to let sounds from the loud-speaker reach the microphone, for the resulting feedback may produce "sing" loud enough to wreck the speaker. It is safer to do your listening with headphones.

Microphones of the condenser type work well in experiments of this kind. They are costly, but for a few cents you can make a crude

one which will pick up the footsteps of insects. Sandwich a sheet of cleansing tissue about four inches square between two sheets of aluminum foil. The cleansing tissue acts as a springy insulator. The weight of an insect walking across one of the foil sheets compresses the tissue, changing the distance between the plates and hence altering their capacity to hold electrical charge. If the condenser is charged, the variations in capacity will produce alternating currents which can be picked up and made audible by your amplifier. Use a 180-volt battery to supply the charge, connecting it in series with a 30-megohm resistor. The resistor in turn should be connected across the phono-input of the sound system through a tenth-microfarad capacitor. The capacitor is inserted in the ungrounded lead of the phono-input. The capacitor insulates the battery from the amplifier. To prevent unwanted noises from entering the system, put the insect, the microphone, battery, resistor and capacitor in a closed wooden box wrapped in a one-inch-thick blanket of rock wool and then pack the whole business into a metal box which will serve as an electrical shield. Connect the microphone assembly to the amplifier with a length of coaxial cable, grounding the outer conductor to the metal box and the chassis of the amplifier. The completed "microscope" is sensitive enough to make the hopping of a flea sound like a cannonade!

If you enjoy weird sounds of this sort, you will not want to miss the "dawn chorus." You can listen to it most easily by picking up a copy of the remarkable recording Out Of This World, prepared by the Cook Laboratories of Stamford, Conn. To hear it directly, you hook a 300-foot length of wire to the ungrounded terminal of your amplifier's phono-input. You must also install a filter which discriminates against 60 and 120 cycles plus all odd harmonics through the 13th, and another to keep out frequencies of 19 kilocycles and above. Millett G. Morgan of the Thayer School of Engineering-at Dartmouth College, who has made extensive observations of ionospheric sounds, recommends that the antenna slant upward, with the outer end supported as high as possible. He also suggests that the experiment be made in the country as far as possible from power lines and that you use batteries for power-in short, minimize electrical noise as much as possible. In effect your audio amplifier is substituted for a radio set.

Hi-fi fans who are interested mainly in the reproduction of music may enjoy constructing the simple instrument shown in Figure 5. It is a power output meter. With it-and a recording of the frequencies between 40 and 15,000 cycles-you can measure and chart the electrical response of your entire system, from pickup to loud-speaker. In addition, you can calibrate the volume control of the amplifier and make quantitative records of the level at which each recording sounds best.

To check the electrical characteristics of the system, you connect the input terminals of the meter across the voice coil of the loud-speaker, start the recording and, when the first frequency come on, adjust the 2,000-ohm variable resistor until the pointer of the milliammeter registers close to the mid-point of the scale. If the response of the system is "flat," subsequent frequencies will produce identical meter readings. If your system is properly adjusted, however, the response will not be flat. It should conform with one of the standard curves adopted by the recording companies.

Operating the toggle switch will cut in the network of resistors and drop the meter reading three decibels. This loss can be compensated by increasing the volume control of the amplifier. The interval through which the control must be turned represents a three-decibel step. This can be marked on the dial. The attenuating network is then switched out of the circuit and the sensitivity of the meter lowered by adjusting the 2,000-ohm resistor until the pointer is again centered. This cycle is repeated until the volume control is fully calibrated. The load represented by the loud-speaker varies with frequency, depending upon the speaker's characteristics, and will influence the accuracy of the calibration. You can eliminate this variable by substituting a "dummy" load for the speaker-a fixed resistor of the same resistance value and power-dissipating capacity as the speaker.

Bibliography

ELEMENTS OF ACOUSTICAL ENGINEERING. Harry F. Olson. D. Van Nostrand Company, Inc., 1947.

HIGH FIDELITY TECHNIQUES. John H. Newitt. Rinehart Books, Inc., 1953.

Suppliers and Organizations

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