An elegant example is the hydroacoustic amplifier devised by Chichester Bell, a cousin of Alexander Graham Bell. With only a thin stream of water playing against a flexible diaphragm, Bell generated continuous sound waves and amplified faint sounds such as the ticking of a watch. In short, his apparatus performed at least two basic functions of the electronic amplifier.

In making his amplifier Bell exploited surface tension: the tendency of a liquid to take the shape that minimizes its ratio of surface to volume. A solid stream of water tends to break into spherical drops-the shape of minimum surface-to-volume ratio. Assume, for example, that a solid stream about the thickness of a pencil lead proceeds from a nozzle for a distance of six inches. It has the form of a long, thin cylinder.

Cylinders present minimum surface when their length and diameter are in the ratio of four to three. Accordingly the stream first breaks into a succession of small cylinders of this proportion, to develop a series of deepening constrictions that at one stage resembles a string of sausages. After the water has proceeded for a distance that depends upon the velocity and diameter of the stream, the constrictions develop and the stream breaks into a series of elongated drops. These oscillate in three dimensions with diminishing amplitude until their kinetic energy is transformed into heat, at which point they become spheres.

Bell observed that the constrictions do not necessarily start to develop the instant the water leaves the nozzle. Although the shape of the stream is highly unstable, the forces associated with surface tension tend to remain in equilibrium. But they are easily disturbed. Equilibrium can be upset, for instance, if the apparatus is vibrated. If the nozzle is displaced abruptly as little as a millionth of an inch, a corresponding constriction will travel down the stream and initiate the formation of a drop. Random vibrations of at least this intensity are normally present everywhere. For this reason jets of water characteristically break into drops of random size.

Bell insulated the jet from random vibrations by inserting the nozzle in a soft rubber tube that also supplied the water. Under a pressure of five to 10 pounds an unbroken stream .05 inch in diameter would proceed for a distance of roughly five inches. Bell then directed the jet against the middle of a thin, flexible diaphragm about an inch in diameter and spaced the nozzle at a distance such that constrictions in the stream were on the verge of developing at the point where the water struck the diaphragm. The force of the jet caused the diaphragm to bow inward slightly. This force was constant. Accordingly the diaphragm, though bowed, did not vibrate. With the apparatus adjusted to this sensitive state a faint vibration communicated to the nozzle would be reproduced as an amplified movement of the diaphragm. Each disturbance of the nozzle caused a constriction to develop that deepened as it traveled down the stream. Upon arriving at the diaphragm the constriction exerted less force than the full stream. Moreover, the depth attained by the constriction and the force exerted on the diaphragm by it varied in proportion to the intensity of the initiating vibration through a significant range of frequencies. As a result of the diminished force the diaphragm would move in the direction of its unstressed position and communicate its movement to the surrounding air as a sound wave. Bell maximized the acoustic efficiency of the apparatus by coupling a horn to the diaphragm.

To make the apparatus oscillate, or sing, he attached a second diaphragm to the nozzle. A random mechanical vibration initiated the first constriction and resulting sound vibration. Part of the acoustic energy would feed back and impinge on the diaphragm at the nozzle, start a second constriction, and so on. The pitch of the resulting sound was determined largely by the resonance of the diaphragm-and-horn assembly.

Complex sounds were amplified by coupling the vibrating source or input signal to the nozzle mechanically. Speech could be reproduced by directing the voice against a diaphragm linked to the nozzle by a stiff wire. The input diaphragm was shielded acoustically from the output to prevent feedback and oscillation. The ticking of a watch could be amplified to fill a room merely by resting the case of the watch lightly against the side of the nozzle

A simple version of the apparatus calls for a tin can with the ends cut out for supporting the output diaphragm, and a nozzle made from the glass tip of a medicine dropper. The nozzle is pushed into the end of a quarter-inch rubber tube connected to a water tap. The can and tube are mounted on wooden supports attached to a base as depicted in the illustration in Figure 1. If the apparatus is to be used more than once, the wooden parts should be waterproofed by a coat of melted paraffin or shellac.

The diaphragm may be made of any thin plastic sheet, such as Saran Wrap. The material is placed over one end of the can like a drumhead and is secured by a tight rubber band. After the band is in place the edges of the material are pulled down uniformly until the diaphragm is tight enough to ring when the side of the can is tapped lightly.

Some medicine droppers end in a small bulb. These will not work. To remove the bulb hold the tip in a gas flame until the glass softens uniformly. Then grasp the bulb with a pair of tweezers, remove from the flame and pull the glass straight out about an inch. Nick the extended part with the edge of a file at the point where the tapered bore is about the diameter of the lead used in mechanical pencils (.05 inch) and break by bending the glass in the direction that exerts tension on the nick. Insert the modified nozzle in the rubber tubing and assemble on the wooden support, allowing about half an inch of rubber between the inner end of the nozzle and the wood.

If possible, equip the rubber tubing with a needle valve for adjusting the flow of water. The system can be "tuned" by regulating the amount of water admitted to the nozzle. A needle valve provides fine control. The apparatus will operate for about 10 minutes on a quart of water. It can be set in a rectangular cake pan to catch the runoff.

A hydroacoustic amplifier made in this way is not likely to take prizes in a hi-fi contest. The frequency response is comparable to that of early acoustic phonographs. That it works at all, however, is astonishing.

Another fascinating oscillator, one that is activated by heat, is described by Julius Sumner Miller, professor of physics at El Camino College in California. "Push a cup of fly screening about a quarter of the way into a l5-inch length of metal pipe an inch and a half in diameter," he writes. "The screening can be held in place with a spring steel ring, as shown in the accompanying illustration [Figure 2 ]. Now hold the pipe vertically (with the screen end down) over a Bunsen flame, the burner of a gas stove or even a large candle, so that the screen is heated. This takes only a few seconds. Remove the pipe from the flame but continue to hold it vertically. It sings! Shift the position of the screening and try the experiment again. With repeated trials a position can be found that causes the pipe to sing loudest. The critical location will be found to lie somewhere between a fifth and a quarter of the length of the pipe-between three and four inches in the case of a 15-inch pipe. Make a second pipe of other dimensions, say 12 inches long and an inch in diameter. Fit it with screening and heat both pipes simultaneously. When the pipes are removed from the flame, each will sing at its characteristic pitch, and a wavering beat note will be generated.

"Now let us explore the physics of this astonishing business. The physics of sounds maintained by heat is not simple, but in general the requirement is that energy be applied intermittently to the air. In the case of the screened pipes, heat is applied to produce periodic convection currents in the air. Consider the situation at the instant the pipe is removed from the flame. The screening is red hot, and heat is radiated to the air in the immediate vicinity. As this air expands it sends a wave of compression up the pipe. But the density of the heated air is reduced. Consequently a rarefaction is formed. The void is promptly filled by an upward rush of cold air from beneath the screening. This air is similarly heated and the cycle repeats. If the heat is maintained (for example, by passing an electric current through the screening), the pipe will sound continuously. When the screen is heated in the manner suggested, however, the sound is heard only briefly.

"Why is the location of the screening important? As mentioned, the operation of the device depends on the fact that heat can set air in motion. In this case the air moves in two ways. First, the entire column drifts slowly up the pipe by convection, just as hot gases move up a chimney. Second, sound waves are generated in the pipe, with the result that the molecules of air oscillate at the ends of the pipe but stand still in the middle, where the node of the sound wave (the point of varying compression ) is situated. The node of sound vibration in the pipe is precisely the reverse of the node associated with a vibrating string. In the latter the nodes ( points of maximum compression) are situated at the ends, where the string is attached, and the antinode (point of maximum excursion) is in the middle of the string. The most favorable position for the screening in our pipes is in the middle of an antinode. This is an acoustic position and does not necessarily correspond to the physical geometry of the pipe It must be found experimentally.

"What kind of pipe and screening should be used? The material is not critical. Ordinary water pipe will work, or aluminum tubing. The latter is easy to cut. Copper or bronze fly screening works well, as do the various metal gauzes. There is no need to measure the initial position of the screening. Just push it into the pipe a little way. If the pipe does not sing on the first try, push the screening in a little farther and try again. The same effect, incidentally, can be observed by using an alternate scheme, one rather more difficult to make work. If hot air is fed into the bottom of the pipe and a piece of screening in the upper part of the pipe is left cold, the pipe will also sing.

"A comparable effect, although one caused by a different mechanism, can be observed by holding a cardboard tube (of any length, diameter and wall thickness) over a gas burner of the Meker type [see illustration in Figure 2]. These burners resemble the more familiar Bunsen burner but have a heavy wire grid across the top. The flame is short, intense and situated above the grid. The tube sings as long as the flame persists. Here the physics of this action differs somewhat from that of the metal pipes fitted with screening. As in the case of the pipes, however, the addition of heat to the air in the immediate neighborhood of the flame gives rise to a pressure change, and a sound wave is set up in the tube. The pulse of high pressure reduces the convective flow of gas through the grid of the burner and so starves the flame momentarily. When the pressure wave has passed, convection carries a fresh supply of gas through the grid, the flame regains its former intensity and the cycle repeats. Heat energy is thus developed discontinuously. Depending upon the size of the burner and the resonant frequency of the pipe, the oscillations can acquire enough intensity to extinguish the flame As with the screened metal pipes, the most effective position for the burner is found experimentally. If the tube is lowered over the burner too quickly however, the flame is almost certain to go out. Incidentally, a stovepipe, a gutter pipe and even a cast-iron water pipe can be excited this way and made to emit a surprising volume of sound.

"Another amusing oscillator, one that involves buoyancy rather than acoustics, can be set up with one or more small vials, some baking powder and a jar of water. It is a new version of the Cartesian diver, the device that is encountered as a toy or as an apparatus by which biologists measure the metabolism of minute living systems such as microorganisms. The conventional Cartesian diver consists of a vessel that contains a bubble just large enough to make the diver float. Any change in atmospheric pressure at the surface is communicated to the liquid inside the diver and compresses the bubble or causes it to expand. This alters the specific gravity of the diver and it sinks or rises accordingly.

"How is this principle used by biologists? In one kind of study an investigator wishes to know the rate at which a microorganism evolves gas in the process of respiration. To measure the rate at which gas is evolved a culture of the organism is incubated inside a minute diver that has been balanced at an intermediate level between the top and bottom of a glass vessel containing a transparent liquid. The evolved gas displaces liquid in the diver, thus altering its specific gravity, and the diver rises proportionately.

"The effect can be approximated on a large scale by putting enough baking powder in a stoppered vial to make the vial sink at the rate of about an inch per second. A 10-milliliter vial with a diameter of one centimeter and a screw on plastic cap works well. Unless the precise displacement and weight of the vial is known, the amount of baking powder required must be determined by trial and error. After the vial has been charged with baking powder, a hole approximately .05 inch in diameter is drilled through the center of the plastic cap. Then the vial is placed upside down in a jar of water [see illustration in Figure 3].

"After the vial has rested on the bottom for a moment, a bubble of gas forms at the hole and continues to grow until the bottle and attached bubble acquire enough buoyancy to rise to the surface. (Baking powder contains sodium bicarbonate mixed with either an acid or a salt; it liberates carbon dioxide when water is added to it.) Watch the bubble carefully when the diver begins to rise. (We say that it 'rises.' Actually it is pushed up by the surrounding water, which is pulled down by the force of gravity.) As the diver proceeds upward, the water exerts progressively less pressure on the bubble, which, obedient to Boyle's law, expands at an increasing rate. The bottle therefore picks up speed and, because of turbulence, gyrates a little. The motion is violent enough to detach most of the bubble when the diver breaks through the surface. The diver then sinks. Be sure to observe the small bubble that remains attached to the cap. On the way down the bubble disappears into the bottle, demonstrating that hydrostatic pressure increases with depth. After the diver rests on the bottom for a moment, the pressure of the accumulating gas overcomes the hydrostatic pressure, the bubble appears and the diver makes another round trip to the surface. Its up-and-down motion will continue for half an hour or more, depending on the size of the bottle.

"Not all the effects that arise from hydrostatic pressure are easy to visualize. About a century ago, for instance, a natural philosopher who saw little point in confronting theory with experiment drew a picture in his mind's eye of how water would flow from a container with three holes in its sides: one hole near the bottom, a second hole above the first and a third hole the same distance above the second. He concluded that the stream from the bottom hole would squirt farthest because the hydrostatic pressure would be greatest at the bottom. The middle stream, according to his reasoning, would not travel quite so far as the bottom one before striking the surface on which the container rested, and the uppermost stream would land closest to the can. He thereupon proceeded to publish his observation, together with a diagram similar to that second from the left in the accompanying illustration [Figure 4] His view won wide acceptance and has been perpetuated down through the years in physics books, including one that received worldwide distribution as recently as 1957. When the question is put to nature in the form of an experiment, however, the streams are found to behave as depicted by the diagram third from the left in the illustration. Where did the philosopher make his mistake?

"It is, of course, easy to overlook the obvious. Consider the game, sometimes offered at carnivals, in which a bystander is invited to knock down a bowling pin with a wooden ball that is suspended by a string [see Figure 5]. The carnival barker demonstrates the game and explains the ground rules. The bystander is instructed to swing the ball so that it misses the pin on the forward swing but knocks it down on the return swing. It all looks very easy, because the barker knocks the pin over every time. The innocent who pays a dime for a try never succeeds because he observes only one of the ball's two motions as it leaves the barker's hands. He sees it swing but he fails to note that the barker first winds up the string so that the ball unwinds in transit and therefore spins in addition to swinging. When swung without spin the ball follows an elliptical path with the pin inside it. When the ball is spun, it responds to the Magnus effect, the aerodynamic force that is exerted on a spinning sphere (or cylinder) at right angles to its trajectory through the air. The same effect explains why a spinning baseball curves. In the case of the carnival game the spin warps the elliptical path just enough to bring the ball into contact with the pin on the return swing, as experiment will convincingly demonstrate.

"One can similarly go astray by failing to take all factors into account when interpreting even the most obvious laws of physics. Consider the law established by Galileo that states in effect that bodies of various masses fall at the same rate. Is it possible for an object that moves solely under the force of gravity to exceed the velocity of free fall? An entertaining apparatus can be constructed to prove that the answer is yes.

"Consider a stick standing on end on a table top. If it falls over, all points on it describe circular paths and all points on it have the same angular velocity. Clearly, however, all points do not have the same linear velocity. (It is assumed that the lower end of the stick does not skid but remains fixed as though on a hinge.) Because all points on the stick have the same angular velocity at all times, it is obvious that all points have the same angular acceleration at all times. But if the angular acceleration is everywhere the same, then the linear acceleration is everywhere different.

"Hence if some point on the stick falls at the velocity of free fall, other points must fall at either a greater or lesser velocity. The velocity of fall at the hinged end is obviously zero. It is reasonable to assume that some point between the hinged end and outer end would attain the velocity of free fall. If so, however, the outer end would necessarily exceed the velocity of free fall.

"To test this assumption hinge a pair of sticks as shown in the accompanying drawing [above]. Open them to an angle of more than 35 degrees and cut a prop to support the upper stick at this angle. Make a small depression in the top of the upper stick near the end to support a small weight such as a marble or a steel ball. Then find the point on the lower stick directly below the depression and mark it with an X. Measure the distance between the X and the outer end of the lower stick. Cement a paper cup to the upper stick at this distance from the outer end. (When the sticks are closed, the cup should be centered over the X on the lower stick.)

"To make the experiment, open the sticks and insert the prop. Place the weight in the depression and quickly remove the prop. The outer end of the upper stick will drop away from the weight as the cup moves into position to catch the weight at the end of the fall. The end of the stick has dropped faster than the weight, which was in free fall. What is observed here, incidentally, explains why tall smokestacks usually buckle as they fall."

Bibliography

700 SCIENCE EXPERIMENTS FOR EVERYONE. UNESCO Source Book for Science Teaching. Doubleday & Company, Inc., 1958.

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