The first experiment comes from George Stibitz, a consultant in applied mathematics who lives in Potter Place, N.H. "It is well known," writes Stibitz, "that the principles governing the transmission of vibrations through elastic tubes also apply in the case of the transmission of signals on telephone lines. Among these principles is the familiar one that only those frequencies present in the driving function can be found in the propagated signal. No direct current will appear in the line, for example, unless direct current is developed by the generator.

"The validity of this principle can be investigated by an easily assembled hydraulic analogy. First join a length of rubber tubing approximately a quarter of an inch in diameter to a length of clear tubing of glass or rigid plastic. The soft tubing can be a foot long. Heat the hard tubing at a point a foot from the joint and bend it into a right angle. Next place a heavy block of wood in the center of a dishpan so that the top of the block extends about an inch above the edge of the pan. Place a vertical support, such as an apparatus stand, near the edge of the pan and attach the free end of the hard tubing to the support as shown in the accompanying illustration [below].

"The support assembly can be calibrated to serve as a manometer for indicating water pressure Fill both the tubing and the pan with water and rest the joint of the tubing on the block as shown. Now provide some means for vibrating the soft tubing near the point at which it joins the hard tubing. I use a Vibro-Graver as the power source. The block serves as an anvil. When the vibrator goes into action, it is obvious that the water in both tubes must oscillate around fixed positions because the system contains no valves. It is also obvious that the average pressure in the tubes must be zero and that no steady flow could occur.

"To test this assumption turn on the vibrator and observe the manometer. A word of caution: Unless you have made the manometer tube several feet tall be sure to stand back or you will get wet! A steady stream of water will shoot from the orifice at an average pressure of several pounds per square inch.

"A startling fact is that this system acts like a pump with valves of some 200 percent efficiency, whereas if there were valves, none of them could be expected to perform with even 100 percent efficiency. In the case of my own apparatus I have measured the 'stroke' of the vibrating element; that is, I worked the vibrator by hand and measured the resulting displacement of water, which is about .1 cubic centimeter per stroke. The vibrator runs at 120 cycles per second. With perfect valves the output should amount to 12 cubic centimeters per second, or 720 cubic centimeters per minute. An actual run produces some 1,500 cubic centimeters per minute. If the vibrator is moved along the soft tube, a point can be found at which the direction- of the pumping reverses. Still further displacement of the vibrator in the same direction restores the flow to its original direction but at a lower volume.

"An explanation of the pump's paradoxical behavior is found in the phase relations of the vibrations in the two sections of tubing. The rigidity of the system is not symmetrical around the point of vibration. For this reason water in the hard tube does not necessarily vibrate in step with that in the soft tube, and a net longitudinal vibration appears at the point where the impulses are applied. Synchronized with this longitudinal vibration is a variation in resistance to flow that is set up by the deformation of the soft tubing. When pressure is applied at the proper point, the soft tube is squeezed during that portion of the cycle when the water is flowing from the hard tube into the soft one, and the soft tube is expanded when the water is flowing in the other direction. The combined actions generate a unidirectional flow.

"The effect caught my eye quite by chance when I was working on a pneumatic pump I invented for producing a flow of blood in superficial arteries. I spent two weeks finding out why the effect occurs. Mathematically there appears to be no limit to its efficiency. By 'tuning' the vibrator a little-varying both the pressure and the point at which vibrations are applied to the soft tube- one can doubtless make the system perform at higher efficiencies than I have observed."

James H. Wiegand of Sacramento, Calif., calls attention to the equally strange behavior of high-polymer fluids 3 subjected to a shearing force. A second force develops at right angles to the shearing force; this phenomenon is known as the Weissenberg effect. According to Wiegand, the second force arises from the tendency of the giant molecules constituting the fluid to return to their normal orientation when they are deranged by the force of shear. The effect can be demonstrated by an apparatus Wiegand described in the Journal of Chemical Education for September, 1963.

Wiegand clamps a vessel such as a drinking glass in a metal fixture that is in turn held in the chuck of a hand drill supported vertically by an apparatus stand. When the drill is turned, the carefully centered glass spins in the normal, upright position around its vertical axis. A stationary glass tube about two centimeters in diameter is also clamped to the stand so that it extends coaxially down into the glass to within a few millimeters of the bottom [see illustration Figure 2].

For the high-polymer solution Wiegand dissolves seven grams of unflavored Knox gelatin in 35 milliliters of water heated to about 130 degrees but not to more than 140 degrees Fahrenheit. When the gelatin has dissolved and the solution has cooled to about 90 degrees, the mixture is transferred to the drinking glass. If the glass is now rotated, the fluid will behave in the expected manner: it will climb the wall of the glass as the surface assumes a paraboloidal shape. When the fluid has cooled to about 86 degrees, a remark able effect begins to appear. A portion of the fluid climbs the outer surface of the stationary tube and simultaneously rises inside the tube at the expense of fluid adhering to the wall of the rotating glass. The effect becomes more pronounced as the temperature continues to drop. Finally the column inside the tube grows by the upward movement of the liquid from the bottom of the glass. If rotation is continued until the contents have chilled to the gel point (82 degrees F.), the center tube becomes solidly plugged. The plug can be removed easily by warming the glass. Other fluids can also be used to demonstrate the phenomenon, including polyisobutylene and the thick fraction of egg white. Wiegand prefers gelatin, primarily because of its availability and ease of preparation.

Not all paradoxical effects such as those represented by the valveless pump and high-polymer fluids that seem to defy gravity are "real" in the sense that physical forces account for the observed behavior. Some must be ascribed to faulty perception. An example is submitted by Arthur Schlang of Mineola, N.Y. It involves an interesting three-dimensional variation of the familiar reversing-cube illusion.

In its commonest form the illusion consists of a perspective drawing of a cube made by connecting the adjacent corners of two overlapping squares by four straight lines. As one looks at either one or the other of the two points within the figure where three lines meet, the perspective of the cube seems to change. Usually the eyes must come to rest for a few seconds on one or the other of the points before the illusion of reversal occurs. Schlang constructs a real cube of wire, with a short length attached at one corner to serve as a handle; it is aligned with the diagonal between the near and the far corner of the cube [see Figure 3 ]. The wires are soldered together at the corners.

To see the illusion hold the handle between the forefinger and the thumb of one hand with the cube at the normal reading distance and, with one eye closed, look at the far corner of the cube. Within a matter of seconds the orientation of the cube will appear to reverse, as in the case of the perspective drawing. When the reversal occurs, roll the handle slowly between finger and thumb. The cube will appear to turn backward! Open the closed eye. The cube will instantly snap back to its true orientation.

Now hold the handle vertically with the cube on top. Again close one eye and fix attention on the far corner. When the illusion of reversal occurs, incline the cube away from you until the handle is horizontal. During this movement the wire handle will appear to bend at the point at which it is attached to the cube and the cube will swing upward until it seems to perch on one corner at the tip of the handle. Roll the handle. Now the cube appears not only to turn in the wrong direction but also to rotate on its vertical axis as if driven by the handle through a pair of crown gears, which change the angle of drive by 90 degrees. One can also equip the cube with a "synchronous satellite." Place a small object such as a cork on a wire and attach the wire to the handle of the cube so that the cork is about an inch above the equator of the cube (assuming the south pole to be the corner to which the handle is attached). When the illusion of reversal occurs and the cube is rotated, the cube and its satellite will appear to move in opposite directions. A little experimentation will disclose a number of other unexpected effects, including a set of interlocking curves that assume various forms when the unit is turned rapidly and viewed from different angles. The curves show up best if the cube is made of polished wire.

The experiment strikingly discloses a role of binocular vision in the perception of shape, position and distance. Under most circumstances the geometry of a scene can be judged adequately by one eye, which reports the relative sizes of objects, their characteristic patterns of light and shade and their relative apparent motions as well as variations in the intensity of lighting between near and far objects. For this reason a one-eyed person is not impossibly handicapped when viewing most objects and can place a considerable amount of confidence in his visual perceptions. A three-dimensional object that is depicted by a perspective drawing in two dimensions is really a monocular representation and appears practically the same whether viewed by one eye or two. That monocular vision does not always convey enough information about the real world for accurate perception, however, is indicated by the fact that the illusion of reversal ordinarily does not appear when the wire cube is viewed by both eyes. (A few people find, incidentally, that they cannot achieve the reversal even with one eye.)

Many seeming paradoxes would vanish if we were endowed with sharper, more reliable eyes. As matters stand the experimenter must often base his conclusions on indirect evidence Students of the flight of birds long wondered, for example, how large birds such as turkey buzzards manage to fly effortlessly above unbroken plains on sunny days of flat calm. Ultimately, by using the visible motion of the birds as indirect clues to air movement, some observers concluded that the birds were carried aloft by vortex rings. These rings, which can attain quite large dimensions,, form when local masses of heated air in contact with the surface detach and float upward, much as bubbles originate in a pan of gently boiling water. To stay aloft soaring birds merely circle in the local updraft that constitutes the core of the vortex ring [see "The Soaring Flight of Birds," by Clarence D. Cone, Jr.; SCIENTIFIC AMERICAN, April, 1962]. Although such rings can ascend at a rate of many feet per minute, their movement has little effect on the neighboring air. In many respects they behave like solid objects. Even when projected at high velocity through still air, however, they do not create a breeze.

These properties can be investigated with a simple vortex-ring generator that has been improvised from a coffee can by Tom Clements of Hightstown, N.J. He uses a can of the type that comes with a polyethylene top. A centered hole about an inch in diameter is cut in the bottom of the can [see Figure 5 ]. Vortex rings are projected from the hole by tapping the plastic top. The rings can be made visible by filling the can with smoke. (To make a generator for producing smoke, heat until soft one end of a glass tube into which a cigarette will slide easily and draw the glass to a gentle taper. Light the cigarette and drop it into the tube so that the unlighted part seats against the taper. Blow into the large end of the tube.)

To demonstrate how vortex rings propagate through still air, make a detector by constructing a grid of fine silk threads suspended from a horizontal bar. A grid a foot square with threads at half-inch intervals works well. Shoot vortex rings at the grid at distances ranging from one foot to 10 feet. Observe how all threads remain undisturbed except those directly in the path of the ring. Observe also how the ring expands comparatively little during its flight. Note how the rolling motion of the vortex ring picks up air in front of it, pushes it aside and finally deposits it relatively undisturbed in its wake as if the ring were a fully streamlined body.

The energy of a vortex ring can be demonstrated by shooting a ring at a lighted candle. Even a comparatively small ring will blow out the flame at a distance of a few feet; large ones will break soap bubbles 15 feet away To prove that the observed properties of the rings do not arise in the smoke, repeat the experiments without smoke. How do vortex rings behave when they strike obstructions such as hard walls? What happens when two collide head on? The answers to such questions are left to the ingenuity of the experimenter [see "Quantized Vortex Rings in Superfluid Helium, by F. Reif; SCIENTIFIC AMERICAN, December, 1964].

Jets of air also exhibit properties on which interesting experiments have been based. Shortly after the introduction of gas lighting in the 19th century, for example, musicians observed that sustained notes of certain pitch, such as those in the upper register of the cello, would cause the lights to dim! Eventually, after much investigation by such British physicists as John Tyndall and Lord Rayleigh, the cause was traced to the instability induced by sound waves in the laminar flow of gas constituting the jet of the burner. By carefully regulating the gas pressure they found it possible to produce jets that would resume laminar flow at the end of a disturbance. With such jets they made an apparatus for investigating the shape of sound waves. It was a primitive but surprisingly effective counterpart of the modern oscilloscope.

Burners for generating these "sensitive" flames can take many forms. I make one version by heating to softness one end of a glass tube roughly eight millimeters in diameter and pulling it into a hairlike capillary. A nozzle is then formed by breaking the capillary at a point about .005 inch in diameter. I use gas from the tank of a propane torch and adjust the pressure for a flame about two centimeters high that floats some 10 centimeters above the nozzle. AS part of the adjustment procedure it is usually necessary to increase the diameter of the nozzle by the cut-and-try method of snipping off additional bits of glass. A properly adjusted flame is blue at the bottom and tipped with yellow. Sustained sounds of 400 cycles and higher, such as the A note above middle C on the piano, cause the flame to drop about two centimeters toward the nozzle. A sharp sound, such as a click, will usually blow out the flame. Even a snap of the fingers will do so at distances of up to 30 feet.

The instantaneous response of sensitive flames can be demonstrated by observing the flame as reflected by a moving mirror. The mirror provides the equivalent of the horizontal sweep of an oscilloscope. In one arrangement a mirror of the size of those used in automobiles is suspended from its upper corners by a pair of threads and set into wobbling vibration around its vertical axis with a push on one end. The flame is seen in the mirror as a ribbon of reflected light. When a sustained sound is projected against the base of the flame, the sound waves appear as undulations along the upper edge of the ribbon. A more convenient horizontal sweep can be made by mounting a set of eight pocket mirrors around the periphery of a wooden disk that can be continuously rotated on a centered vertical shaft. The mirrors successively sweep the image of the flame across the field of view in the direction of the rotation

Sensitive flames can also be made to function as oscillators for generating sound waves. For these experiments I use a nozzle about a millimeter in diameter and adjust the jet so that it is on the verge of instability-the point at which the flame changes from the smooth shape of a candle flame to one that flares and roars. If a pipe about two inches in diameter and two feet or more long is now lowered over the flame, a point will be found at which the apparatus sings. The pitch of the tone depends on the distance between the flame and the end of the pipe. The sound is initiated by some random event that triggers instability. The resulting compression wave then traverses the pipe and is reflected back to the jet from the end, initiating the next cycle.

Another interesting oscillator, also powered by heat, is known as Trevelyan's rocker. It consists of a specially shaped block of hot metal in contact with a thin strip of lead. The combination will sing a minute or longer if the block has been heated close to the melting point of lead.

A version of the apparatus made by Roger Hayward, who illustrates this department, consists of a rectangular block of brass about half an inch square and three-quarters of an inch long. A groove is filed in one of the corners to form a pair of knife edges spaced three-sixteenths of an inch apart, as shown in the accompanying illustration [above]. The other end of the block is drilled for a push fit with a brass rod six inches long and an eighth of an inch in diameter. A second block of any metal is similarly drilled for a push fit with the other end of the rod. The lead block must have a single knife edge.

When the knife edges of the heated brass block are placed at right angles across the knife edge of the lead block, the brass-block assembly promptly goes into torsional vibration and emits continuous sound at about 100 cycles per second. The vibrations are generated primarily by the lead. It is almost impossible to place the brass on the lead so that each of the two brass edges bears equal weight. Therefore initially one brass edge transmits more heat to the lead than the other. The lead expands with enough violence to rotate the brass so that somewhat greater pressure is then exerted between the other brass edge and the lead. This volume of lead now absorbs heat at an accelerated rate and expands, rocking the brass in the other direction and initiating the next cycle. The rate of vibration is established by the natural resonance in torsion of the masses that are coupled through the elastic rod.

Bibliography

EXPERIMENTAL SCIENCE. George M. Hopkins. Munn & Co., 1890.

THE SCIENTIFIC AMERICAN BOOK OF PROJECTS FOR THE AMATEUR SCIENTIST. C. L. Stong. Simon and Schuster, 1960.

THE THEORY OF SOUND. John W. S. Rayleigh. Dover Publications, Inc., 1945.

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