SOME SOUND PHENOMENA CONNECTED WITH GUN-FIRE
By Commander Garrett L. Schuyler, U. S. Navy
This discussion of some of the simpler points in the sound phenomena of gun-fire is in no sense original. In fact, the theory was clearly stated and published years ago, although until the war it was of no special popular interest. Since then, however, these phenomena have taken on a new interest, because so many at the front heard them and occasionally their safety depended upon an intelligent understanding of them. One is impressed by the great extent to which those of all ranks in various armies who have had active service with artillery know the facts connected with the peculiar noises heard, even if in all cases they have not heard much about the reasons for them. In the navy this information is for many reasons much less widely diffused. There are certain striking and easily remembered conclusions which we may well spare a minute or two recalling to mind, or which might be included in future text books on naval gunnery. There are one or two special naval applications of the phenomena that may be mentioned, and a few popular fallacies which can be disposed of. One may therefore perhaps be pardoned for referring here to phenomena which are so largely a matter of common knowledge.
A projectile moving at a high velocity generates a sound wave of conical shape with the projectile always at its point. It is quite analogous to the V-shaped bow wave that a ship makes when under way. Bow wave analogies are perhaps the easiest way to illustrate the sound phenomena. For low speeds the sides of this conical sound wave make a large angle with the axis of the projectile, just as at slow speeds the bow wave of a ship is pushed along and stands out at a large angle on either bow. High velocity projectiles make a conical sound wave of a more acute angle, just as at high speeds the bow wave of a ship extends behind at a much smaller angle with the keel. The semi-angle of the wave, that is, the angle between the direction of motion of the object producing it and the line of the advancing wave front, diminishes as the speed increases. The sine of this angle is the ratio of the velocity with which the disturbance is propagated in the particular medium, and the velocity with which the object producing the disturbance moves. If, for example, the projectile moves twice as rapidly as sound travels, the sound wave extends out at 30° on each side of the projectile, 30° being the angle whose sine is one-half. This can be verified by a simple geometrical construction. As an origin, take a point on the paper and assume that it represents the location of the projectile at a selected instant. The idea is to construct the form of the sound wave at the time when the projectile is at that point. On some appropriate scale mark back from this origin the path by which the projectile arrived. On this line choose other points at intervals, each representing the projectile at certain earlier instants. Take each of these points and consider the time the projectile took to get from it to the origin. See how far, according to the scale, sound would travel during this interval of time. From the point draw a circle of radius equal to such a distance. The envelope of these circles, or the line which could be drawn around just touching and enclosing all of them, will thus define the wave front at the time when the projectile is at the origin.
If the projectile is moving at a constant speed, then the radius of each circle and the corresponding distance from its center to the origin will compare in the ratio of the velocity of sound and the velocity of the projectile. If the projectile moves at a varying rate, or on a curved path, the wave front will not be composed of these two straight lines, but will be somewhat distorted, just as the bow wave would be from a ship in deep, calm water if it steered a changing course and went at a varying speed. By laying it out in detail the special form of the sound wave in any given case can be readily arrived at.
We have many evidences that this conception of a conical sound wave being generated by a high-velocity projectile is reality, and not a mere hypothesis. Spark photography is perhaps the most convincing evidence. A projectile moving in the dark touches two small wires and causes an electric spark of extremely short duration to be made just over it. A sensitized photographic plate lies below it and a shadow picture is made. On the shadow picture a silhouette of the projectile, which was illuminated for only the briefest interval of time, is shown clearly and dark with very distinct edges. Perfectly sharp lines represent the sound wave previously described. This representation of so intangible an object as a sound wave results from the fact that the density of the air in it is greater than the density of the air around it. The index of refraction in a sound wave is different. Consequently rays of light passing through this region from the spark to the photographic plate are slightly deflected in passing. They turn differently, and so on the photographic plate no ray arrives which would pass directly from the spark in a straight line through any portion of the sound wave. There is a dark line on either side, as sharp and clear as the shadow from a wire. Knowing the velocity of sound and measuring the angle between the sound wave on either side and the axis of the projectile, we can estimate the velocity of the projectile. The velocity of the projectile can be measured by other means, and the agreement is a convincing check on the correctness of the theory.
When on the front one hears an enemy long-range gun dropping shells in his vicinity, there is at first a loud report, then a whistling noise and then the report of a shell exploding. Many are likely to think that the first report heard is caused by the discharge of the gun. If the matter is studied it will be found that in general this report occurred so closely before the fall of the projectile that it could not possibly have come from the gun and arrive so soon after the projectile. Furthermore, this first report is much too loud to come from a distant gun, particularly with an unfavorable wind. Yet it is always heard in any kind of weather. It is merely the sound wave from the projectile.
Experienced observers in well established parts of the front can tell with surprising accuracy just where projectiles are landing. The sound which reaches an observer seems to come from close on either side of a point in the trajectory where the component of the projectile's velocity resolved toward the observer is equal to the velocity of sound. If on one day the enemy is shooting low and on another day the projectile is a little higher, in both cases the point from which this false report apparently originates is very nearly in the same place as regards the observer. In the two cases, however, the distance that the projectile travels beyond these points before exploding on the ground may vary considerably. Hence the interval between the sound of the false report and the sound of the projectile bursting may be quite different in the two cases. It may be, for example, an interval of four seconds in one case, and eight seconds in another. It is quite easy for the trained ear to distinguish, and the difference is sufficient to indicate with surprising accuracy where the projectiles are going. It should be understood that the estimate is made not by working out by formulas, but in a simple practical way. The observer finds out on different occasions where the projectiles are landing, and remembers, or notes down, what it sounds like. If he hears that sound again, he knows where the projectile is falling to cause it. It requires no intelligence, but only a memory, and many do it very well without being able to tell how they do it. It is interesting, perhaps, for those of us in the navy to know that this can be done, though it may not have any special naval application.
Another thing that should not be lost sight of is that the false report comes from a point which is not in general between the observer and the gun, and therefore, if he tries in this way to guess the location of the gun which is firing projectiles landing to one side of him, he will be entirely misled. Of course, if he knows where the guns are he can recognize one or the other by the similarity of its sound and the sound which he previously heard from it; but he could not locate a new gun in this way. It would be much like an observer off a port in a small boat in calm, foggy weather, feeling the bow wave of a steamer which had just come out of port and was passing near him in the fog. If it were an old experience he could compare it with what he had experienced before, but without previous experience he could tell the direction from which the bow wave seemed to come to him in the fog but this would not indicate to him the direction of the port from which the ship had started. Artillerists are always cautioned not to do this kind of guessing unless they know where the guns are and have heard them before. This does not, however, apply to very distant firing, such as a general action miles away. In that case we hear the guns themselves, rather than passing projectiles, and it is possible to make a very fair estimate of the direction of the artillery activity.
In naval gunnery where the remaining velocity of the projectile is greater than the velocity of sound, it follows that one will never hear the approach of the projectile which strikes him. It is the same thing as the proposition that a relatively motionless ship is not going to be rammed by a high-speed vessel which does not change its course and from which we experienced the passing wave.
A fallacy which one often hears is that the impact of projectiles on the water makes a loud noise like a report. Those who hold this view have usually arrived at it from noting that on target practice there is a loud report, which is not the discharge of the guns, and which can be heard on the towing ship at about the time the projectiles strike the water. They assume that this impact is what makes the noise. It is nothing more than the sound wave of the flying projectiles which reaches them.
Although usually only the false report made near the end of the trajectory is heard, it is possible under certain conditions to hear more than one such report. This is particularly true in very curved trajectories. It is no more difficult to comprehend than would be the arrival of bow waves at different times at a small anchored boat from a large vessel steaming around near it with considerable variation of course and speed.
If a projectile falls short of us the wave continues on and reaches us, as explained before, and the report is not a noise caused by the impact of the projectile on the water. A wave generated in the air has simply travelled on and reached us. It is like a vessel coming towards us at high speed, and suddenly stopping engines and anchoring. If not too far away her wave would leave her and travel on to reach us. It would not be a disturbance generated by the ship stopping, but would be the arrival of a disturbance previously accompanying the ship but continuing on after the ship had stopped.
In naval gunnery when we are near guns firing (either on the same ship or on one with it in formation) echoes often return. It is surprising what an excellent reflector of sound the side of a near-by ship can be. This is often noted with boats passing near the proving ground.
When one is fairly close to a gun which is firing he often hears a double report. One is the false report from the projectile, the other is the report from the gun. Illustrating by analogy with waves on water, it is much like dropping a heavy toy boat into a tank and immediately starting to tow it along. There would be a circular wave from the original splash where the toy boat fell in and started from, and there would be the V-shaped bow wave which it carried along while being towed. We could select many points where both of these waves would be experienced separately, and in some places where they would be experienced separately they would be of very nearly the same character. Thus, it is not surprising that in the field at certain distances, and on certain bearings from a gun, a single gun may sound like two guns being fired. This happens sometimes at sea.
The principal conclusion that we can draw from this discussion is that all points of the theory of the sounds are well understood and were worked out years ago. There are very great differences in the characters of sounds which we are likely to hear on shore with artillery. This enables artillerists to tell a great deal from sounds, but their success depends almost entirely upon knowing local conditions, knowing where the enemy's guns are, and, having heard something which they can find out about, remembering what it sounds like so that it can be recognized if it is heard again. At sea these advantages are not possible, and noises from gun-fire, in themselves, can tell us little. We can, however, judge approximately the direction of distant firing. The sharp report just before the projectile lands would be a most misleading indication of the direction from which it had come. One could not hear the arrival of the projectiles which strike the ship. On occasions, double reports may be heard. The reports which one hears on target practice when projectiles strike the water are not made by impact, although it often seems as though such were the case.