# 1922 Encyclopædia Britannica/Sound

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​SOUND (see 25.437).—The increase in our knowledge of the subject of acoustics (the science of Sound) during recent years has been largely associated with the war conditions which prevailed from 1914 to 1918. As a consequence of the war the development of this science has been abnormal, and research has been directed towards the rapid realization of practical acoustic devices and methods for immediate use in warfare, both on land and sea. A general survey of the work done shows that the advances consist of applications of well-established principles, rather than the discovery of new phenomena. Generally, the observations made have proved to be in accordance with previous theoretical investigations, mainly due to the late Lord Rayleigh. This war work falls naturally under two headings, viz. (1) the detection and perception of direction of sounds in air, and (2) the detection and perception of direction of sounds in water. Theoretically, these two problems have much in common, but, practically, there are important differences which make it desirable to treat them in separate sections. A special section (3) is devoted to the important advances recently made in auditorium acoustics, and the remaining section (4) deals briefly with miscellaneous outstanding features of modern work on sound, not essentially military in character.
I. DETECTION AND PERCEPTION OF DIRECTION OF SOUNDS IN AIR
Detection.—The human ear itself is a remarkably sensitive detector of the air vibrations which constitute sound. It is still much superior in this respect to any mechanical device which has yet been produced for recording the vibrations visually. Thus the perception of feeble sounds of necessity depends upon the limitations of audibility, either indirect listening, or with the ear aided by the intervention of an electrical device such as a microphone. The audibility of a feeble sound can be very largely augmented by making use of the principle of resonance, provided that the sound itself approximates to a pure tone. This can be secured, for example, by the use of a Helmholtz resonator applied to the ear in the case of direct listening, and in addition, by tuning the diaphragm receiver when microphonic listening is adopted. It has happened fortuitously that one of the chief sounds in air which it is important to be able to detect, viz. those emitted by aircraft, do contain predominant notes which enable the application of resonance, as above indicated, to increase largely the range of audibility. Typical predominant frequencies (apparently due to engine exhaust) are given in the following table, which relates to the engine running at the usual speed:—
| Aeroplane engine | Frequency (vibrations per second) |
| S. E. 5 | 130 |
| R. E. 8 | 90 |
| F. E. 2B | 70 |
| Avro | 90 |
| Gotha | 80 |
The following frequencies have been detected in the sounds from the Maybach engines of a Zeppelin airship:—
Slow speed—27, 54, 108, 135, 243.
High speed—57, 114, 171, 228.
The operation of the Doppler effect, arising from the relative motion between the aircraft and the observer, prevents the possibility of the identification of the machine by means of the observed frequency, this being liable to change by as much as 20%, according to the speed and direction of flight. An interesting observation which has been constantly made is that the notes of low pitch continue to be heard at ranges where those of high pitch have ceased to be audible. This is in accordance with the theoretical expectation that damping increases with frequency.
The determination of the direction whence a sound arrives is theoretically possible by a variety of methods dealt with below, several of which have been tried in aircraft localization.
(a) Binaural Listening.—Lord Rayleigh's experiments (Collected Papers, vol. 5, p. 347) have shown that low-pitched sounds are determined in direction by the observation of the phase difference between the vibrations arriving at the two ears. This principle has been applied in direction-finding, and the effect has been exaggerated by increasing the distance between the two points of reception. The sound is received by two equal trumpets or horns rigidly connected together and capable of rotation about an axis perpendicular to the line joining them. Separate and exactly equal tubes lead from the trumpets to the two ears, respectively, and the apparatus is rotated until the sound under observation appears to come from directly in front. The line joining the sound receivers is then perpendicular to the incident sound stream. An alternative method which dispenses with the necessity of rotating the apparatus is to use a compensator or phase-measurer, which consists of tubes, adjustable in length, inserted between the sound receivers and the appropriate ears, so as to provide a path difference equal to that between the distant source of sound and the tworeceivers. Adjustment of the tube lengths is made until the impression received is that the sound is neither to the right nor to the left, and the determination of direction is then a matter of simple geometry. In practice the compensator is graduated to give direct angular readings.
The practice of binaural listening has verified theoretical conclusions in several important respects. It has been found that it is easier to perceive the direction of a mixed sound, or noise, than a pure note. Apparently it is necessary that the wave train should contain more or less isolated special characteristics whereby the phase difference can be readily appreciated. In the regular sine wave corresponding to a pure tone each vibration is exactly like those which immediately precede and follow it, and the ears are unable to identify corresponding displacements. It is apparently also necessary for successful binaural listening that the two portions of the incident wave which enter the two receivers should be free from subsequent distortion; in particular, that the sound receivers should be as nearly as possible non-resonant for the vibrations in question. Any amplification of the sound which depends upon resonance, therefore, such as the use of Helmholtz resonators already referred to, is incompatible with efficient direction-finding by observations of phase difference.
The construction and arrangement of the receivers used has varied very much in practice. As a typical system, that commonly used in the British army may be quoted, namely, circular cones, 2 to 4 ft. long and of semi-angle 20, as receivers, placed about 7 ft. apart—a distance which proved to be sufficient for attaining nearly the maximum practical accuracy of setting.
The method is subject to many errors, chiefly those arising from the motion of the sound source, refraction due to temperature inequalities in the air, and the effect of winds. The necessary corrections are tabulated for use in practice.
(b) Sound Mirrors.—Some success has been attained in direction-finding by means of concave sound reflectors. The chief limitations have arisen from the question of size, and, consequently, of ​portability. In optics the size of mirrors commonly in use is very great in comparison with the wave-lengths of the light; in the corresponding problem in acoustics it is almost impossible to make them so; and yet this is a necessary condition for the geometrical laws of reflection to apply with accuracy. In the largest sound mirrors—perhaps 20 ft. in diameter—the size is at most only a few wave-lengths for the aircraft sounds under investigation, with the result that the image of a distant sound obtained at the focus proves to be an area much larger than that corresponding to optical calculations. There is therefore no advantage secured by making the mirror paraboloidal instead of spherical, and considerable roughness of the surface is not detrimental. The mirrors were usually made of concrete, and listening was effected either by means of a small horn receiver placed in the focal plane and connected by a tube to the ears, or by means of a microphone placed in a similar position. If, as was more usual, the mirror was fixed, the direction of the sound source could be found by determining the position of maximum intensity in the focal plane. It may be noted that in this method of direction-finding amplification is obtained on account of the area of the mirror, and that further augmentation is attainable by using resonators, to which the same objections do not apply as in binaural listening. The accuracy of the determinations vary very much with frequency, being much greater for notes of high pitch than for low, as would be anticipated from considerations of wave-length.
(c) Interference and Diffraction Methods.—There have been many attempts to apply the principle of interference as a substitute for binaural listening, i.e., by ultimately mixing the sounds entering the two receivers, instead of leading them to different ears, and adjusting the compensator until the total sound heard is as loud as possible. Theoretically this will occur when there has been provided in the compensator a difference of path equal to the path difference outside the receivers. The method has not proved very successful, for a variety of reasons, some of which are obscure. We shall not elab- orate them here.
On the other hand, remarkable results have been obtained by the application to sound waves of a phenomenon well known in the diffraction of light. A small distant source of light gives in the middle of the shadow of a small circular obstacle a luminous region, called the "white spot," arising from the diffraction of light round the edges of the obstacle. The same phenomenon is observable in sound under suitable conditions. Thus a large horizontal disc, at least 20 ft. in diameter, and made of material which either reflects or absorbs sound, will give below itself a sound shadow of a sound source, such as an aeroplane, above it. Near the centre of the shadow, in a position depending on that of the source, there is a region where the sound heard is comparatively loud—in many cases much louder than it would be if the disc were absent. The relation between the direction of incidence of the sound and the position of maximum intensity has been calculated, and the method provides, perhaps, the most reliable means of perceiving the direction of air-borne sounds.
(d) Sound Ranging.—This special military aspect of the localization of sound sources, viz. those arising from gun-fire and shell bursts, is dealt with in the article RANGE-FINDERS.
2. DETECTION AND PERCEPTION OF DIRECTION OF SOUNDS IN WATER
Of all the methods practised for the detection of submarines that depending on the sounds which they emit has been of the widest application. The question of detection has been, of course, of nearly equal importance in the opposite sense, viz. the hearing of surface ships by the crew of a submerged submarine. The sounds created in the sea by a screw-propelled ship are of a very complicated character, arising partly from the interaction between the propeller and the water, and partly from the vibrations of the machinery which are transmitted through the walls of the ship into the sea. They vary greatly from ship to ship, even of the same class; and, in the later stages of the war, submarines had been constructed which, when cruising submerged at certain slow speeds, emitted practically no noise at all. In many ways the detection of submarines in the sea is more difficult than that of aircraft in air. Normally, listening in air takes place at stations which are fixed; in submarine listening the stations were most frequently ships, which for tactical reasons connected with their safety, had to be constantly on the move. Their own machinery noise and the acoustic disturbances arising from their motion through the water were very apt to drown the noises proceeding from more distant sources. The noise of the sea, too, even in weather not at all stormy, interfered greatly, and the range at which a submarine could be heard varied much from day to day. A serious additional limitation was that recourse could not normally be had to the reflection of ordinary sounds (as is possible in air) chiefly by reason of the great size of the necessary reflectors. For the speed of sound in sea water is more than four times that in air, so that the wave-lengths are larger in the same ratio. This necessitates a corresponding increase in the linear dimensions of the sound mirror, if equal efficiency is to be obtained.
Hydrophones.—Hydrophones, or under-water sound detectors, were already in use before the war for signalling purposes, being carried by ships for listening to submarine bells operated by Trinity House as warnings in foggy weather. They consisted of small, metal, water-tight cases of which one face was a metallic diaphragm operating an enclosed microphone. The electrical disturbances of the microphone caused by any vibration of the diaphragm arising from sound pressure waves in the sea, were conveyed to telephone receivers on the ship, where listening took place. It was usual to suspend the hydrophones in water-filled tanks attached inboard to the outer shell of the ship, which, owing to the fact that steel in water transmits sound almost completely, does not diminish appreciably the intensity. Normally the hydrophone diaphragm was tuned so that its natural frequency in water approximated to that of the signalling bell, and so that increased range could be secured by depending on resonance.
The earlier hydrophones used for naval purposes were of much the same type, although the resonant diaphragm proved to be by no means an unmixed advantage. All sounds containing a component corresponding to the diaphragm frequency were distorted in reproduction, and what was gained in sensitivity was liable to be lost in the difficulty of recognition, or, in other words, failure in discrimination between genuine noises due to a submarine and other noises inevitably present in the sea. Appeal to resonance is only really advantageous when the sound under observation has a predominant note, as in the case of an aeroplane; and submarines do not display this characteristic. Ultimately hydrophones of a non-resonant character came to be preferred, and were frequently used in practice. These consisted most usually of enclosures made of rubber, sufficiently thick to withstand the pressure of the sea at the usual depth (about 15 ft.), and having natural frequencies below the limit of audition.
An alternative type of hydrophone consisted merely of a hollow enclosure without a microphone, sometimes with a metallic diaphragm, and sometimes simply a rubber tube, filled with air and connected by long tubes to stethoscopes applied to the ears. These are operated by the transference of the pressure vibrations from the sea to the air cavity and thence to the ears. Electrical hydrophones have the advantage over non-electrical ones that their sensitivity can be readily augmented by various means, e.g., bv the use of thermionic amplifiers (see WIRELESS TELEGRAPHY).
In cases where the hydrophones had to be used by ships in motion, they were sometimes fitted into the hull of the ship; or themselves consisted of fish-shaped bodies towed at a considerable distance behind the ship. The former precaution, i.e. making the shape stream-like, aimed at diminishing the vibrations created by the passage of the hydrophone through the water; the latter had in view the partial elimination of the disturbances arising from noises in the towing ship. Even so, it frequently became necessary to stop the engines temporarily, and listen with the towed hydrophones while the momentum of the ship continued to carry it forward. This proved to be only feasible at comparatively slow speeds.
Directional Hydrophones.—All the hydrophones so far described are of a non-directional character, i.e. the intensity of the sound heard in them is practically independent of the orientation of the sensitive receiving diaphragm with respect to the position of the source of sound. The limitations of dimensions necessitated by considerations of portability, etc., are such as to render the instruments much too small to give an effective "sound shadow." The reason for this has already been mentioned, viz. the great wave-lengths corresponding to audible sounds. At a frequency of 500 per second, for example, the wave-length in water is nearly ten feet.
Differential Hydrophones.—Curiously enough, however, one type of directional hydrophone, called here for distinguishing purposes a differential hydrophone, did, in fact, depend upon the small differences of pressure operating upon its two sides; and it met with considerable success. It was made in various forms, the simplest of which consisted of a circular metal diaphragm, bearing at its centre a water-tight box containing a microphone, and clamped round its rim to a heavy metal ring. When placed in the sea so that the plane of the diaphragm passed through the position of the sound source, the pressure variations on the two sides are the same both in amplitude and phase, with the result that the diaphragm and therefore ​the microphone, has no motion imparted to it, and the sound heard is a minimum. If, however, the diaphragm faces the sound source, there are, apparently, differences in the pressures on the two sides (probably in both amplitude and phase), and a small differential vibration takes place, with consequent sound in the receiving telephones. Actually, as the hydrophone is rotated through 360° about a vertical axis, two maxima and two minima of sound intensity are observed. In this form, therefore, the instrument is what is called bi-directional, i.e. it is unable to distinguish between sources in front and behind. The desirability of obtaining a uni-directional instrument led to the introduction of the so-called baffle-plate, the behaviour of which has not yet been explained satisfactorily in terms of orthodox theory. The essential characteristics of a baffle appear to be that it should be made of non-resonant material and have air cavities within it. Such a plate, fixed at a small distance (which has to be determined by trial) from one face of a bi-directional hydrophone, transforms it into a uni-directional instrument. A single sound maximum is now obtained upon rotation, occurring when the sound source and the baffle plate are on opposite sides of the diaphragm; and a single minimum, this when the baffle lies between the sound source and the diaphragm. The " edge-on " minima, observed when the baffle is absent, now disappear.
Binaural Listening. The principles underlying this method of direction-finding have been described already. In the present case the main difference is that the sound receivers have to be submerged hydrophones. It has been found to be equally necessary for success that these should be as completely as possible non-resonant. The simplest arrangement used in practice was two rubber cavities placed several feet apart horizontally, and joined by separate equal tubes to the two ears. The device could be rotated about a vertical axis, usually passing through the hull of the operating ship. As in the case of air listening, compensators were often used in order to avoid the necessity of rotating heavy apparatus. An arrangement much preferred was to tow two or more fish-shaped hydrophones in known positions (about 12 ft. apart) behind the ship. Here electrical transference of the acoustic disturbances had to be adopted, and this necessitated great care in the choice of the microphones and telephone receivers so as to avoid selective resonance. (The behaviour of microphones in this respect was often unsatisfactory, and telephone earpieces, or magnetophones, were frequently substituted for them. This results in diminished sensitivity, but the binaural effects are much improved.) The telephone receivers delivered the sound into the compensator, and the phase difference was measured in the usual way; allowing, of course, for the difference of speed of sound in the sea and in the air channels of the compensator. In using a compensator with two sound-receiving units only, there remains an ambiguity of estimated direction, i.e. one cannot distinguish between the angles θ and π + θ. The introduction of a third unit, so that the three form a triangle of known dimensions, the units being capable of use in pairs with the compensator ensures the correct choice between the alternative angles.
Other Methods of Direction-finding. Several other methods of perception of direction, not easy to classify, have found application in practice. One of these consisted in fitting in the shell of a ship, on opposite sides, two diaphragms with microphones attached, arranged so that the hydrophones thus formed were of as nearly as possible equal sensitivity. These were listened to alternately by means of a reversing switch. The ship, on account of its considerable size, was capable of giving a marked sound shadow. Thus the starboard hydrophone would give greater response than that on the port side if the sound source were to starboard, and vice versa. By steering the ship so that the responses were equal, it could be inferred that the course was directed towards the cause of the sound. The limitations of the method were mainly those arising from local noises; and the speed had to be small while listening took place.
In other cases large numbers of sound receivers, usually simple diaphragms whose function was to transfer the vibrations from the sea to the air inside, were inserted in the ship's hull. Good results were obtained by an arrangement of this kind, called the Walser gear, in which the sound receivers were disposed at regular intervals on a large bulge, in the shape of a spherical segment, incorporated in the hull on either side towards the bows. The system acted as a sound lens, a sound focus occurring at a point where the "sound paths" by alternative routes were equal. Application of the laws of geometrical optics enabled the relation between the position of the focus and the direction of incidence of the sound wave on the ship's side to be determined.
Sea Sound-Ranging. The methods hitherto mentioned for perceiving sound direction would all fail when the sounds are abrupt in character, because they all require an appreciable time for carrying out the necessary tests. To determine the position of an exploding submarine mine or torpedo we require, therefore, a different device. A suitable method is one identical in principle with that practised on land. The main variations in applying the device to the sea are that the microphones must be in submerged hydrophones, and that a correct knowledge of the velocity of sound in sea water must form the basis of the calculations. Ordinary non-directional hydrophones of the type first mentioned have proved to be quite sufficiently sensitive. Indeed, the greatness of the distances at which explosions in the sea have given unmistakable impressions on the recording film has been surprising. Small detonators serve at distances of several miles, while the explosion of 40 lb. of gun-cotton is operative more than 100 m. from the receiving hydrophones. Many experiments have been carried out by the British Admiralty with hydrophones disposed in suitable positions on the East coast of Britain, and the installations promise to be useful, not only for locating mine and torpedo explosions in circumstances of war, but also for navigational and surveying purposes. A ship in fog, for example, could ascertain its position by exploding (with due notification by wireless to the sound-ranging station) a small charge near itself in the sea; the station could within a few minutes inform the ship again by wireless of its position.
Sea sound-ranging has necessitated the accurate redetermination of the velocity of sound in sea water. This has been accomplished by the inverse of the process just mentioned, viz. by exploding charges in the sea, and measuring by the recording string galvanometer the time intervals between the reception of the first shock by hydrophones submerged in accurately known positions. The observed velocity depends on several factors, including tidal flow, temperature, and salinity, which vary from place to place. The following table gives some of the results obtained, corrected to a standard salinity corresponding to a specific gravity of 1.-026 and a temperature of 10°C.:
| Date | Place | Corrected Velocity in ft. per sec. |
| 16.5.18. | Dover | 4.882 |
| 6.11.18. | Dover | 4.921 |
| 18.7.18. | Dover | 4.924 |
| 26.7.17. | Culver (I. of W.) | 4.962 |
The effect of tide, apparently, has not been allowed for. It would amount, at most, to a few feet per second.
3. AUDITORIUM ACOUSTICS
The acoustics of public buildings have recently been put on what approximates to an exact scientific basis, largely as a result of the work of W. C. Sabine (Frank. Inst. J., 179, p. i, 1915). For good hearing three conditions are necessary and sufficient. The sound heard must be loud enough; the simultaneous constituents of a mixed sound must preserve their relative intensities; and the successive sounds must remain distinct and in the correct order, and be free from extraneous noises. The extent to which these conditions are fulfilled depends on the construction of the auditorium, its shape, its dimensions, and the materials of which it is composed. In already finished buildings radical alterations of the first two are not often feasible, but great improvements can be secured solely by suitable changes in the internal features.
The main difficulty arises from what has been called reverberation, due to the multiple reflection of sound at different parts of the room. If the reverberation is prolonged, it means that the rate of absorption of the sound is slow. Thus, in a lecture room at Harvard, where these experiments were commenced, the rate of absorption was so small that a single spoken word continued to be audible for 55 seconds. Successive syllables thus had to be heard and appreciated through a loud mixed sound due to the reverberation of many previous syllables, and the conditions of hearing were intolerable. Great reduction of the multiple echoes constituting reverberation can be made by increasing the rate of absorption of sound. It is apparent that, in the space of several seconds, the sounds travelling at 1,100 ft. per sec. will have suffered many successive reflections, and will, therefore, have penetrated to practically all parts of the room. The sound will have become diffuse radiation, and absorbing material introduced almost anywhere will be equally effective in reducing reverberation. An open window proves to be a complete absorber, in the sense that it permits the egress of the maximum possible quantity of sound radiation (cf. the properties of a small aperture in an isothermal enclosure in heat radiation). The introduction of cushions, carpets, wall hangings and people also largely diminishes reverberation, because of their considerable absorbing powers. Sabine has made a systematic study of the coefficients of sound absorption of various materials by the inverse method of measuring their effect in reducing the duration of reverberation. Typical results are given in the following table. These apply to the frequency an octave above middle C. ​
| Material | Coefficient of Absorption |
| Open window | 1.000 |
| Linoleum, loose on floor | 0.12 |
| Oriental rugs | 0.29 |
| Plaster on wood lath | 0.034 |
| Glass, single thickness | 0.027 |
| Plain ash chairs | 0.008 |
| Upholstered chairs | 0.30 |
| Hair felt, 2.5 cm. thick, 8 cm. from wall | 0.78 |
Other measurements indicated that an audience gave an absorption equal to 44% of that due to an equal area of complete absorber, thus accounting for the improved hearing conditions known to exist in well-filled buildings.
The absorption of sound can thus be adjusted with precision, but it must not be carried too far, otherwise the sound intensity is too much diminished. The ear is able to disregard, or even to take advantage of, reverberation which is not too prolonged, and the extent of absorption has to be adjusted to the appropriate amount. Too many apertures such as open windows or doors must be avoided.
Sabine has also made examination of the exact manner in which sound is reflected in an auditorium by constructing scale models of the latter, and photographing the sound waves at various instants after creation, using the beautiful method due to Toepler (Annalen der Physik, 127, p. 556) and elaborated by R. W. Wood (Physical Optics, 2 ed., 1911, p. 94). By this means the positions of the sound waves, both incident and reflected, are capable of observation at all instants and at all points in the model room, and they provide data upon which can be based correct architectural construction from the acoustic point of view.
4. MISCELLANEOUS ADVANCES
Absolute Measurement of Sound. A. G. Webster (Nat. Acad. Sci. Proc.. 5, p. 173, 1919) has advanced to a considerable extent the methods of absolute measurement. For this purpose it is impossible to rely upon audition, handicapped as it is by the vagaries of the ear. What is required is a reliable mechanical device, the performance of which is constant, to record the sound vibrations with sufficient magnification. Webster has made an exhaustive study of the properties of various materials, and has constructed from those most suitable for the purpose two instruments which he has called the phone and phonometer respectively. The phone provides a means of creating a simple tone of intensity and frequency which are under control and capable of exact measurement. The phonometer is an instrument for measuring absolutely the vibrations received by it. It consists of the combination of a diaphragm and a resonator, both of which are adjustable in frequency. The motion of the diaphragm is observed by making it a reflector and part of a Michelson interferometer, so that the amplitude is measured in terms of the wave-length of suitable monochromatic light. In practice the interference fringes are photographed on a moving film upon which they appear as wavy lines. Against this instrument, which is regarded as a standard, other portable phonometers can be calibrated, these depending on the simpler process of the deflection of a beam of light set into angular oscillation by the receiving diaphragm. With such instruments, and also with D. C. Miller's phonodeik (referred to later) L. V. King has carried out an elaborate investigation on the propagation of sound in air and fog-signal efficiency (Phil. Trans.. 218, p. 211, 1919) in the region near Father Point, Quebec. King, in this paper; also describes a modification of the siren called the diaphone, used as a standard source of sound in his research.
(A. O. R.)
* ↑ Owing to the abnormality of the conditions, it is impossible to follow the usual practices in writing the present article. Experiments on sound, with military ends in view, have been carried out in nearly all the belligerent countries. Comparatively few of the results have found their way into the recognized scientific journals, largely by reason of the secrecy which is still frequently enforced by the various Governments, under whose control most of the work was done. In the circumstances it is not safe to attempt to assign credit to particular investigators, nor is it possible to give adequate references. The present article has been drawn up, therefore, upon broad general lines which, since they fulfil censorship conditions, form necessarily a by no means complete survey; and names have been avoided as far as possible.
* ↑ Lord Rayleigh's work is contained in his Collected Papers (No. 6, 1920). His contributions were numerous between 1911 and 1919, when he died.
* ↑ The information contained in this section is largely drawn from a manual entitled Development of Sounds, kindly placed at the writer's disposal by the British Munitions Inventions Dept.
* ↑ This method of perception of direction has been largely used also in a connexion which scarcely justifies treatment in a separate section. The geophone is an instrument for direction-finding of sounds proceeding through the earth, and its particular use during the war was for localizing the sounds of picks, etc. used in tunnelling and land mining. It consists of two hollow boxes connected by equal tubes to a stethoscope arranged so that the sounds proceed from the two boxes to separate ears. The boxes are laid upon the ground a few feet apart, and moved about until the sounds of the pick appear to come from straight ahead. It is then known that the sound source is on a line perpendicular to that joining the two geophone receivers, since the sounds arrive through the earth in synchronism. By combining several pairs of geophones separated by considerable distances, the actual position of the pick can be estimated, for it lies at the intersection of the several perpendiculars above specified.
* ↑ The following publications should be consulted, although, for reasons already given, they form by no means adequate references:— H. C. Hayes, Engineer (1920), p. 491; C. V. Drysdale (Kelvin Lecture), Journ, I.E.E. (1920); W. H. Bragg, "Submarine Acoustics," Nature, July 1919; F. L. Hopwood, "Submarine Acoustics," Nature, Aug. 1919.
* ↑ This is considerably lower than the natural frequency in air, on account of the additional loading by the water.