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 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&mdash;perhaps 20 ft. in diameter&mdash;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.&mdash;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&mdash;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.&mdash;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.

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.&mdash;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.&mdash;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.&mdash;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