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 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.:

The effect of tide, apparently, has not been allowed for. It would amount, at most, to a few feet per second.

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.