WHIISPERING GALLERIES, which are usually a domed room, are an attraction for visitors the world over. Their distinctive feature is that they carry a sound as soft as a whisper over distances the whisper would not traverse without acoustic aid from the structure. At first the listener finds the effect startling, particularly when he can see the whisperer and so can recognize the improbability of the sound's carrying over such a distance.

The effect occurs mainly in two types of structure. In the simpler type the inside surface of the room is a section of a sphere or an ellipsoid. When a speaker stands at the center of curvature of the sphere, the spreading sound waves are reflected and focused back to him with surprising loudness. If an ellipsoid is involved, the speaker is at one focus and the listener is at the other. Again the curved surface reflects the spreading sound waves and focuses them, this time to the second focal point. In both types of structure a sound can travel through a large volume of air and still remain audible because of simple reflection and focusing.

The second type of whispering gallery is also curved but is more difficult to analyze because it involves no focusing. When a speaker whispers along one of these circular walls, the sound is somehow held in a layer adjacent to the wall; it travels along the wall and can be heard by a listener anywhere on the circumference. Why the sound clings to the wall in this manner and how you can demonstrate the effect for yourself are my subjects for this month, although I should make it clear at the outset that I do not understand all the features of the demonstration.

The most famous whispering gallery of the second type is at the base of the dome of St. Paul's Cathedral in London. The gallery is a walkway about 40 meters above the main floor. The walkway is six feet wide and forms a circle with a diameter of 108 feet. The wall along the side of the walkway is inclined slightly inward. About 40 meters above the walkway is the top of the dome.

Long ago it was noticed that someone whispering along the gallery wall could be heard by anyone who was close to the wall at any point around the walkway. If the speaker whispered directly across the diameter of the circular gallery, however, the spreading of the sound waves made the sound inaudible to a listener on the far side.

The anomalous audibility in the gallery was first brought to scientific attention by Sir John Herschel, who is largely noted for his contributions to optics and astronomy in the first half of the l9th century. Later (in 1871) Sir George Airy, the astronomer royal, explained the effect in terms of simple reflection and focusing of sound waves by the dome. In 1878, however, Lord Rayleigh pointed out that such an explanation could not possibly be correct because it would require the listener to be on the opposite side of the gallery from the speaker. Since the listener could actually be anywhere along the circular walkway, the effect was clearly not due to reflections from the dome.

Rayleigh's first explanation appeared in his Theory of Sound (Volume II, Section 287, published in 1878), in which he drew on his earlier work on the diffraction of sound as it leaves a person's mouth. In general, when sound waves pass through an aperture that has a width comparable to their wavelength, they interfere with one another and create a diffraction pattern. The most intense sound is at the center of the pattern; angled off from the center are alternating regions of destructive interference (corresponding to less intense sound) and constructive interference (corresponding to more intense sound, although not quite as intense as the sound in the central region). A similar diffraction occurs when sound waves pass an edge or move around an object of a size comparable to the wavelength.

When someone speaks, the sound coming from his mouth forms the pattern because the sound diffracts first through the opening of the mouth and then backward around the head. It is more difficult to determine the pattern than it would be if the sound went through a single aperture in an otherwise solid surface, but for the moment we can simplify the pattern by concentrating on the central peak of intensity in an idealized experiment with a single aperture. The angular width of the central region depends in part on the wavelength of the sound: the longer the wavelength (the lower the frequency). the more spread the central region. If you are to hear a person making sounds primarily of shorter wavelengths (higher frequencies), the person should be facing you, otherwise you will not be in the central region of the diffraction pattern. If the voice of the person speaking consists primarily of longer wavelengths, you can still hear the sound well even if he is partly turned away from you, because diffraction makes the central region wide enough so that a significant amount of sound is sent to the side of the speaker and even to the rear.

Rayleigh pointed out that to demonstrate the whispering-gallery effect on St. Paul's walkway a person had to whisper along the wall. Since whispering consists only of high frequencies, most of the sound emerged in a fairly narrow cone along the wall. For the sake of simplicity let us consider the cone as having two dimensions rather than three and as lying horizontally, so that we can ignore the vertical spread of the sound.

The sound leaves the wall in a cone of rays forming a maximum angle of with a tangent to the wall. The rays reflect from the curved wall at various points along the circumference in such a way that with each reflection the angle of reflection equals the angle of incidence. Because the rays began in a cone of angle they remain in a region bounded on the outside by the wall and on the inside by an imaginary wall with a radius that is the radius of the real wall multiplied by the cosine of B. The rays are therefore trapped in a layer along the wall and can be heard by a listener in that layer but not by someone outside it. In this model the thickness of the layer is determined by the radius of curvature of the gallery and by the maximum angle at which the sound leaves the wall when the speaker whispers along it. That angle is in turn determined primarily by the diffraction of the sound coming from the speaker. The higher the frequency, the smaller the diffraction pattern: the smaller the maximum angle is, the more closely the sound is confined to the wall.

When sound from a small source spreads out in a plane in free space, its intensity drops off as the inverse of the square of the distance from the source. With the multiple reflections in Rayleigh's model for St. Paul's gallery, however, the intensity diminishes only as the inverse of the first power of the distance. Hence the sound remains stronger as it travels around the wall than it would if it were sent directly across the gallery. The sounds of lower frequency in normal speech do not contribute as noticeable a layer of clinging waves because their diffraction from the speaker's mouth spreads them over such a thick layer that a listener somewhere around the wall will intercept a smaller action of the original intensity. Rayleigh's model was appealing because of its simplicity; as we shall see, however, its simplicity is somewhat misleading.

In 1904 Rayleigh returned to the whispering-gallery effect, working with a laboratory model consisting of a long strip of zinc (12 by two feet) bent into a semicircle. Inside one end of the strip Rayleigh placed a birdcall whistle and at the other end a flame that was sensitive to the pressure variations produced by sound. When the whistle was blown, it emitted a high-frequency sound at a wavelength of about two centimeters and caused the flame at the far end of the semicircular wall to oscillate. If Rayleigh placed a narrow barrier (about two inches wide) anywhere along the inside wall of the zinc strip, however, the flame was not disturbed by sounds from the whistle. This result indicated to Rayleigh that sound waves were indeed traveling along the surface of the curved strip rather than passing directly across the semicircle. In a like manner surface waves were traveling along the wall in St. Paul's gallery.

In spite of the success of his model Rayleigh was not satisfied with it. He finally published a wave model of the effect in 1910. He then likened the excitation of the air enclosed by the circular gallery of St. Paul's to an excitation of a circular membrane on a drumhead. In an ideal case the membrane would oscillate in a wave pattern with zero amplitude along the rim (because the membrane is fastened in place there) and amplitudes changing toward the center of the membrane according to an equation involving Bessel functions which are also known as cylinder functions (from the type of problem in which they are helpful).

In a circular gallery a voice or any other noise makes the molecules of air oscillate, causing the air pressure to oscillate. The oscillations of air pressure are what we call sound, since they cause the eardrum to oscillate. The molecules next to the wall cannot readily move (because the wall is in the way), but molecules farther out can. When the oscillating molecules farther out move toward the wall, they squeeze the molecules next to the wall and increase the air pressure. When the molecules move away from the wall, they leave the molecules next to the wall less dense and therefore decrease the pressure. Hence the pressure variations in the layer of air next to the wall are relatively large. With a vibrating membrane on a drum the mathematical condition to be met at the rim is that the amplitude of the vibrations be zero. With air pressure the condition to be met at the wall is that the amplitude of the variations in air pressure be at a maximum. To a listener this result means that the sound has an intensity maximum at the wall. As the listener moves away from the wall the pressure variations and therefore the intensity of the sound die away according to a Bessel function of the listener's distance from the center of the gallery.

On a real drumhead and in a real circular gallery many of these patterns (the Bessel-function solutions) can exist simultaneously. For the sake of simplicity Rayleigh considered the oscillations in the gallery to be due to a single Bessel function of a high order, the high order being necessary so that the oscillations occurred only near the wall and then rather quickly died away with distance toward the center of the circle. (Lower order Bessel-functions would produce oscillations nearer the center.) Such excitation only along the wall was required because the speaker whispered close to the wall, hence creating little or no excitation away from the wall. Rayleigh was thus able to demonstrate that the pressure variations due to the surface waves would be at a maximum at the wall and essentially zero away from it. Moreover, he was able to write an equation that gave the amplitude of the pressure variations as a function of radial distance from the center of the gallery. Once again, however, the simplicity of his results can be somewhat misleading.

John S. Derov, a physics student at Cleveland State University, has performed a series of experiments with surface waves on a curved surface similar to Rayleigh's. The results cannot be as clearly interpreted as Rayleigh's work implied. This means that you can do a lot more work on the experiment if you would like to pursue it.

Derov fashioned a semicircular wall by joining two pieces of sheet metal eight feet long and two feet wide to get one sheet 15 feet long. At the overlap the sheets were attached with pop rivets. The gauge of the metal is not particularly important, except that with a heavier gauge the structure would be sturdier. To support the metal wall in a semicircle on the top of a large table Derov erected eight wood braces behind the wall about two feet apart. To increase the mass and rigidity of the wall he glued some concrete slabs to the outside of it and also stuck on some large slabs of Play-Doh.

Reflections from the room and its contents can tremendously complicate the behavior of sound, and so Derov suspended a tent of blankets over the top and across the front of the semicircle. He replaced Rayleigh's birdcall whistle and sensitive flame with several things. In one set of trials he used a two-inch paper loudspeaker for the sound source and a microphone for the detector. In another set he worked with two three-inch piezoelectric oscillators, one as the source and the other as the detector. He also briefly tried a pair of tiny earphones of the type supplied with some television sets, but their frequency range was quite narrow. In each case the source was driven by a sine wave from an audio oscillator with a controllable volume and frequency, and the signal from the detector was read on an oscilloscope.

A variety of equipment is available if you would like to do this experiment yourself. Primarily you need a source capable of emitting frequencies from about one kilohertz to at least 25 kilohertz, or as close to that range as you can get. The detector need not be anything more than a volume meter of the kind found in some tape recorders. Avoid putting large objects into the experimental setup because the reflections of the sound waves from them can complicate your data. Piezoelectric transducers are often sold in electronic and audio surplus shops as tweeters for stereo systems; they cost about $8 each and are good over the frequency range from seven to 25 kilohertz.

For each set of experiments Derov placed both the source and the detector at equal heights (about halfway up the wall). The source was pointed along the wall; the detector also faced along the wall, although it was occasionally reoriented to test for sound being transmitted directly across the semicircle. As a first check Derov placed the source and the detector at opposite ends of the semicircle as Rayleigh did. Like Rayleigh, he found that the sound was more intense in the layer next to the wall. He also found as Rayleigh did that the sound was easily eliminated by a narrow board placed anywhere along the wall between the source and the detector. Thus both Rayleigh and Derov seem to have found that sound waves cling to the surface of the curved wall as they travel along it.

To systematically analyze the sound near the wall the detector was shifted in two ways. First it was moved along the circumference of the wall to see if the intensity was indeed at a maximum there. Then at various points along the circumference it was moved radially inward to see if the peak of intensity on the wall died out toward the center of curvature. We ran into trouble with the first set of measurements, because Derov immediately found that the intensity along the circumference varied considerably, alternating between the expected high values and some surprising values of near-silence.

Similar variations along the circumference had been observed by C. V. Raman and G. A. Sutherland in 1921 in the whispering gallery of St. Paul's. They placed a continuous, single-frequency source of sound near the gallery wall and then checked the level of the sound at various points along the walkway. Some had a proper loudness but others had near-silence. They attributed this variation to the interference of the waves that traveled around the circular walkway more than once and overlapped other waves. At some points the interference was constructive, yielding a noticeable sound, but at others the interference was destructive, yielding near-silence.

Something similar must have been happening in Derov's setup. It could not have been that waves were traveling more than once around a circular wall, because he had built only a semicircle. The explanation presumably was that some of the waves were coming off the end of the wall opposite the source reflecting from apparatus, the blankets or even Derov himself and then traveling back along the wall in the opposite direction to interfere with the oncoming waves.

To check this possibility Derov put a large piece of acoustic tile (removed from our ceiling) at the end of the wall, angling it to help reflect waves out of the setup. He found that the regions of near-silence were either eliminated or greatly reduced, yielding an almost constant level of volume along the entire length of the wall. If you want to continue the experiment, you should take pains to eliminate the waves reflecting back along the wall.

More difficult for us to explain were Derov's measurements along a radial line. We expected to find that once the troublesome reflected waves were eliminated a detector moved outward in a direction perpendicular to the wall would show a single intensity peak at the wall and zero intensity a short distance away. Instead we always recorded at least two peaks, the largest peak at the wall as expected and one or two more away from the wall.

At first we found these extra peaks dismaying, but on further thought we realized we should probably have expected them for two reasons. First, the sound from the source was not emerging in a narrow cone running along the wall; rather it was diffracting out of the source and then spreading. As a result more than one of Rayleigh's Bessel-function solutions was being excited, creating a net pattern that has both a strong Bessel-function peak at the wall and other Bessel-function peaks away from the wall. Derov was measuring the more complicated composite pattern. Second, reflections of the emerging sound from the tabletop, the apparatus and even the blankets were inevitable and would complicate the data by creating interference patterns whose peaks Derov was apparently observing.

By going to higher frequencies we expected to narrow the diffraction out of the source and thereby to decrease the distance from the wall at which the multiple peaks occurred. Derov's data might have confirmed this expectation to some extent, but the scatter in the data points was too large to make the argument convincing. If Derov had been able to go to even higher frequencies (and therefore shorter wavelengths) with his apparatus, he probably would have come closer to having a single layer of sound along the wall, as Rayleigh did. Nevertheless, the assumption of a single layer of sound is not particularly good even in St. Paul's whispering gallery because Raman and Sutherland also found multiple layers of sound there as they moved their detector radially away from the wall.

You could do a good deal of work with this experiment. First, you could improve on the design by eliminating more of the reflected sounds. For example, instead of mounting the wall on a table you might place it on Styrofoam to absorb the sound. To totally eliminate any reflected signals I suppose you could hang the semicircle outdoors, facing upward in a large open space. You might also want to build a larger semicircle or use an existing architectural structure that has a large radius of curvature. If you do not have access to a larger structure, you probably should try higher frequencies, so that the wavelengths are significantly smaller than the radius of curvature.

In addition to taking data such as Derov's you might want to see how the intensity of the surface waves changes with height along the wall and how the intensity pattern changes if the source and the detector are not halfway up the wall. One of the interesting features of the St. Paul's gallery is that the wall leans slightly inward. Some investigators have suggested that this slanting aids in maintaining the surface waves. By building a wall with a slight lean you might be able to confirm this suggestion. The whispering-gallery effect is supposed to work even with non-rigid structures (although the mathematical modeling is more complicated), and so you could also run the experiment with thin walls for a comparison.

If you are good at electronics, you might want to measure the speed of the surface waves in the normal setup. They travel a bit slower than sound traveling in a straight line, and it would be interesting to see how much slower they are. You could find out by using an oscillator that emits a short pulse of sound (make it as close to a single frequency as you can) and also triggers an oscilloscope. Have the detector plugged into the oscilloscope. The time needed for the pulse to reach the detector starts when the trace begins on the oscilloscope and ends when the oscillation pattern begins

If you visit London, you should try the whispering gallery of St. Paul's Cathedral for yourself. Although I knew what to expect, I found its acoustics amazing. A friend of mine stood on the opposite side of the walkway from me and spoke facing the wall. I could hear her whispers and normal speech in spite of the great amount of noise made by tourists on the walkway and far below in the pews. (It is best to visit the gallery in the winter, when fewer tourists are there.)

The effects seemed most pronounced when my friend and I stood next to the wall, but in normal speech the effect was still present when either or both of us moved toward the railing along the inside of the walkway. Following a suggestion by Robert S. Shankland, an expert on architectural acoustics, I spoke to my friend using words chosen because they result in sounds of either high or low frequency. As I expected, the words dominated by high frequencies were the easiest to understand.

While I was in the gallery I noticed that its wall not only tilts inward but also has a significant lip at the top. Shankland believes these two features must be largely responsible for the gallery's unique acoustics. The many other circular walkways in the world that lack these features do not display the same remarkable acoustics.

Whispering galleries of the simple reflection type can be found in a variety of places. Some, such as the old hall of the House of Representatives in the Capitol Building in Washington, have been famed for their ability to transmit even slight whispers. In 1851 the hall was made into the Hall of Statues and became, as the acoustic expert Wallace C. Sabine once noted, "one of the most perfect of whispering galleries." The ceiling was a portion of a sphere whose center of curvature was almost at head level When someone stood at the center and whispered, the sound echoed back to the center,

focused by the spherical surface Sometimes guides would place one person on one side of the center and another person on the opposite side at about the same distance from the center, whereupon a whisper from one of them would be reflected and partially focused on the other. In 1901 a fire elsewhere in the building led to a refurbishing of the hall, and the smooth wood ceiling was replaced by steel and plaster along with recessed panels and reliefs of moldings and ribs. The resulting roughness of the surface greatly reduced the simple reflection and focusing, and the hall was no longer as good a whispering gallery.

The Mormon Tabernacle in Salt Lake City is almost an example of an ellipsoidal whispering gallery, although the interior shape is not a perfect ellipsoid. Sounds created at the reader's desk in front carry by way of reflection and focusing to the rear of the room, making the sounds audible at the front of the rear balcony.

According to Herschel, a similar focusing in an ellipsoidal interior caused considerable embarrassment to parishioners at the old cathedral of Girgenti in Sicily not long after it was built. Although the details of the interior were later disputed by Sabine, Herschel maintained that one of the interior foci was unwittingly chosen as the place for the confessional, and so anyone standing at the other focus had access to even the faintest confessions. "The focus was discovered by accident," Herschel wrote, "and for some time the person who discovered it took pleasure in hearing, and in bringing his friends to hear, utterances intended for the priest alone. One day, it is said, his own wife occupied the penitential stool, and both he and his friends were thus made acquainted with secrets which were the reverse of amusing to one of the party."

Whispering galleries of both general kinds are thought to exist below the smooth, curved arches of some bridges. In 1948 several such arches were separately analyzed by Herbert Grove Dorsey and Arthur Taber Jones to determine if the acoustic properties were due to Rayleigh surface waves. For example, Dorsey investigated the arch under the Massachusetts Avenue bridge over Rock Creek in Washington, D.C. This circular arch has a diameter of 148 feet and a width of 74 feet. Both ends terminate on a base of smooth concrete that provided sharp echoes, supposedly of Rayleigh surface waves bouncing back and forth from end to end on the arch as they clung to the inside surface. "If one stands close to the arch wall in early-morning quiet," Dorsey wrote, "one can hear two distinct echoes from a faint whisper or from a pin dropped a half-inch into a little pasteboard box." A handclap produced from five to 10 echoes.

Later Jones investigated a similar bridge at Newton Upper Falls, Mass., but was unable to confirm Dorsey's hypothesis that the sound traveled along such an arch as a Rayleigh surface wave does. If surface waves were involved, Jones contended, an observer at the center point under the arch would not hear the echoes generated when another person clapped hands at one end of the arch, since the sound would be confined to a relatively narrow belt just below the surface of the arch. Stationing an observer under the bridge, Jones discovered that the echoes were seemingly as abundant there as at the ends of the arch. Hence the contribution of surface waves to the multiple echoes was left undecided.

Certain natural formations have noticeable whispering-gallery properties. The Ear of Dionysius, a grotto in an old quarry near Syracuse in Sicily, is such a natural formation. The grotto is in the shape of a horizontal backward S, with a total floor length of 67 meters and a height of 22 meters. Along the floor the width of the grotto is about 10 meters, but the S narrows toward the top until the width is only one or two meters. At the end of the S opposite the quarry, near the top of the grotto, a small opening leads to a short passageway, which in turn leads to a stone stairway to the top of the rock formation. When one stands on the floor of the grotto, the echoes from speech are so numerous that the speech is difficult to understand. If one listens at the small opening at the back of the grotto, however, one can hear even whispers from others standing on the grotto floor. Although the grotto is not strictly a whispering gallery of the kind I have been discussing, its design does somehow funnel the sound from the floor to a listener who is strategically placed in the small back opening. The reason for the name Ear of Dionysius is that the grotto was used as a prison by Dionysius, the infamous builder of Syracuse. According to legend, he had a prison designed in such a way that he could hear even the faint whispers of the prisoners and so could thwart any attempt at revolt.

You might want to search for whispering galleries. You could check any obvious sections of spheres or ellipsoids in buildings and natural shapes such as domes in cave ceilings. You might also want to check smooth archways (such as those under bridges), the interior of silos and other large structures with a circular cross section. Once a whispering gallery is discovered you ought to check for Rayleigh surface waves by an appropriate set of experiments such as placing a relatively narrow barrier on the curved surface to block any surface waves.

In the months since an experiment involving the creation of multiple-order rainbows in the laboratory was described in this department for July, 1977, several people have written to me about having seen more than two natural rainbows simultaneously in the sky. The primary rainbow arises from a single reflection of light inside a falling raindrop. The occasional secondary rainbow arises from two internal reflections. In the experiment you can see the next dozen or so rainbows, which arise from a progressively larger number of internal reflections from single water drops suspended on a thin wire.

I had believed observing any natural rainbows beyond the first two was impossible because the colors of rainbows of higher order become so faint that they would be masked by the glare from the sky, from the light reflected from the outside surface of the drops and from light transmitted through the drops with no internal reflections. Still, perhaps under some circumstances rainbows of higher order might be visible.

M. L. Herr of the University of New Orleans recalled seeing more than two simultaneous rainbows, maybe even four, in Malaysia, which often has brief thundershowers brightly illuminated with direct sunlight. Other places such as Ireland are said to be good for brilliant rainbow displays, possibly with more than the first two rainbows, because many showers are lighted by direct sunlight. Such observations would be improbable in places where a thunderstorm usually means that the entire sky is clouded before and after the rain.

J. R. Prescott of the University of Adelaide described seeing what might have been the third-order rainbow under an unusual circumstance. As was demonstrated in my rainbow experiment, the third-order rainbow lies in the portion of the sky near the sun and so is normally lost in glare. Just before sunset Prescott saw colors arching through rain falling from very dark clouds that were high enough in the southwestern sky for the sun to be visible below the clouds. The colors were therefore seen against a dark background while the rain was well illuminated by the low sun. If this sighting was indeed of a third-order rainbow, it means that the rainbow becomes visible when the background is dark enough to keep the background light of the sky from masking the rainbow's colors.

You might want to watch carefully for such a fortunate arrangement of clouds, rain and sun. If you photograph the colored arc, measurements of its width would verify that the arc was truly a rainbow rather than a colored halo or some other atmospheric optical effect caused by ice crystals [see "Atmospheric Halos," by David K. Lynch; SCIENTIFIC AMERICAN, April]. You should also be careful not to confuse rainbows of the fifth and sixth orders, which lie near the first two rainbows, with well-developed supernumerary bows of the primary and secondary rainbows. If you do manage to photograph an authentic higher-order rainbow, it will be the first known photograph of any order except the common first two.

Several groups have worked with the suspended-drop rainbows described in my article. Steve Lai, a student of Fred Brace's in a high school in Portland, Ore., observed quite a few of the higher-order rainbows. To see rainbows of the 10th and 14th orders, which requires looking almost along the incident beam, Lai cleverly aimed a dentist's small mirror to reflect an image of the drops and the rainbows, thereby keeping his head out of the incident beam.

AT this year's International Science and A Engineering Fair, Joseph E. Becker of Spokane, Wash., showed me his work on experimentally determining a function by which the angle of a rainbow of any order can be determined for a fluid of any given refractive index. Three other exhibits at the fair were also extensions of topics taken up in this department. The Leidenfrost phenomenon (August, 1977) of fluid drops floating on a thin vapor layer over a hot plate was investigated by Jerry Ritter, Jr., of Cloudcroft, N. M., and by Stuart A. Travis of Akron, Colo. Ritter was interested in how the Leidenfrost point changes when the water is contaminated with various substances and how a measurement of the Leidenfrost point might serve to indicate the extent of the contamination. Travis measured the Leidenfrost points of distilled water (400 degrees Fahrenheit) and acetone (330 degrees F.) and had good luck photo- graphing the floating drops with a 55 millimeter lens and a 6x extender.

Peter Rathmann of Brookfield, Wis., made an impressive analysis of a salt oscillator (October, 1977) in which he determined the oscillator's frequency as a function of hole size, running time, difference in densities between the salt water and fresh water and other factors. He found that for the range of holes small enough to allow the system to oscillate the oscillation frequency increased almost linearly with hole size.

He also demonstrated that the frequency decreased with the running time of the experiment, a result he interpreted as indicating that as the experiment ran, the difference in density between the two fluids in the oscillator decreased because of mixing and therefore the force driving the oscillations weakened.

Rathmann and independently J. E. Schmidt of Charlestown, Ind., have properly pointed out that in my article I should have emphasized the pendulum-like nature of the salt oscillator. Once the fluid begins to flow it does not stop when the pressures at the hole are equalized, because the flow has momentum and the system overshoots its equilibrium state. Once the stream stops, the system again finds itself with unequal pressures around the hole and fluid begins to run in the opposite direction, again overshooting the equilibrium, slowing to a stop and reversing. The Rayleigh instability I discussed in that article is needed to keep the oscillator going because the viscosity of the fluids tends to decrease the momentum in the streams. Otherwise the pendulum-like oscillations of the system would die out relatively quickly.

Bibliography

WHISPERING GALLERIES. Wallace Clement Sabine in Collected Papers on Acoustics. Harvard University Press, 1922.

THE ECHOES AT ECHO BRTDGE. Arthur Taber Jones in Journal of the Acoustical Society of America. Vol. 20, No. 5. pages 706-707; September, 1948.

THE PROBLEM OF THE WHISPERING GALLERY. John William Strutt. Baron Rayleigh, in Scientific Papers, Vol. V, 1902-1910. Dover Publications,1964. -

WHISPERING GALLERIES. Tom Beer in Contemporary Physics, Vol. 16, No.3, pages 257-262; May, 1975.

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