104 ACOUSTICS umerictil .lite of V air. it y were equal to 1 , V = U, which is the result obtained by Newton, and would indicate that the velocity of sound in a gas equals the velocity of a body falling from a height equal to half of that of a homogeneous atmosphere of the gas. 20. In common dry air at 32 Fahr., g being 32 2 ft., and the mercurial barometer 30 ins. or 2 5 ft., the density of air is to that of mercury as 1: 10,485 - 6; hence H = 10,458-6x2-5 ft. = 26,214 ft. Also 7 = 1-408 Hence V = ^1,408 x 32,2 x 26,214 = 1090 ft. and, by 18, the increase of velocity for each degree of rise / . 1 . 1090 545 of temperature beini 491 . 1090 is - or 982 491 = 1-110 ft. in cliffe- nt gases. xpen- ents for itermin- g V in r. depends i intensity
- .sound.
depends
- i the
itch of mud. 1- ft. very nearly. t/ 21. If the value of y were the same for different gases, it is obvious from formula V = / v - that, at a given v 7 p temperature, the velocities of sound in those gases would be to each other inversely as the square roots of their densities. Regnault has found that this is so for common air, carbonic acid, nitrous oxide, hydrogen and ammoniacal gas (though less so as regards the two last). 22. The experimental determination of the velocity of sound in air has been carried out by ascertaining accurately the time intervening between the flash and report of a gun as observed at a given distance, and dividing the distance by the time. A discussion of the many experiments con ducted on this principle in various countries and at various periods, by Van Der Kolk (Land, and Edin. Phil. May., July 1865), assigns to the velocity of sound in dry air at 32 Fahr., 1091 ft. 8 in. per second, with a probable error of 3-7 ft.; and still more recently (in 1871) Mr Stone, the Astronomer Royal at the Cape of Good Hope, has found 1090-6 as the result of careful experiments by him self there. The coincidence of these numbers with that we have already obtained theoretically sufficiently estab lishes the general accuracy of the theory. 23. Still it cannot be overlooked that the formula for V is founded on assumptions which, though approximately, are not strictly correct. Thus, the air is not a perfect gas, nor is the variation of elastic force, caused by the passage through it of a wave of disturbance always very small in comparison with the elastic force of the undisturbed air. Earnshaw (1858) first drew attention to these points, and came to the conclusion that the velocity of sound increases with its loudness, that is, with the violence of the disturb ance. In confirmation of this statement, he appeals to a singular fact, viz., that, during experiments made by Captain Parry, in the North Polar Regions, for determin ing the velocity of sound, it was invariably found that the report of the discharge of cannon was heard, at a distance of 2 miles, perceptibly earlier than the sound of the word fire, which, of course, preceded the discharge. As, in the course of propagation in unlimited air, there is a gradual decay in the intensity of sound, it would fol low that the velocity must also gradually decrease as the sound proceeds onwards. This curious inference has been verified experimentally by Regnault, who found the velocity of sound to have decreased by 2 2 ft. per second in passing from a distance of 4000 to one of 7500 feet. 24. Among other interesting results, derived by the accurate methods adopted by Regnault, but which want of space forbids us to describe, may be mentioned the de pendence of the velocity of sound on its pitch, lower notes being, cent, par., transmitted at a more rapid rate than higher ones. Thus, the fundamental note of a trumpet travels faster than its harmonics. 25. The velocity of sound in liquids and solids (the dis- Vinliqi placements being longitudinal), may be obtained by formula ^ soli (I.), neglecting the thermic effects of the compressions and expansions as being comparatively inconsiderable, and may be put in other forms : Thus, if we denote by e the change in length of one foot of a column of the substance produced by its own weight f JP ,-, i w ftp , e n , , w, then e being = - or , we have - = - and hence : v= (IV.) or, replacing - (which is the length in feet of a column that would be increased 1 foot by the weight of 1 cubic foot) by I, v=^ . . (v.) which shows that the velocity is that due to a fall through Or, again, in the case of a liquid, if 77 denote the change of volume, which would be produced by an increase of pressure equal to one atmosphere, or to that of a column H of the liquid, since is the change of volume due to weight of a column 1 of the liquid, and .".- = and - II = , we get v- ^ < VI Ex. 1. For water, = 20,000 very nearly; II = 34 ft. V in wn and hence V = 4680 feet. This number coincides very closely with the value ob tained, whether by direct experiment, as by Colladon and Sturm on the Lake of Geneva in 1826, who found 4708, or by indirect means which assign to the velocity in the water of the River Seine at 59 Fahr. a velocity of 4714 ft. (Wertheim). Ex. 2. For iron. Let the weight necessary to double V in ire the length of an iron bar be 4260 millions of Ibs. on the square foot. Then a length I will be extended to / + 1 by . 4260 millions Ibs. , rpl . , . a force of - ; - on the sq. ft. llns, therefore, (/ by our definition of /, must be the weight of a cubic foot of the iron. Assuming" the density of iron to be 7 8, and 62-32 Ibs. as the weight of a cubic foot of water, we get 7-8 x 62-32 or 486 Ibs. as the weight of an equal bulk of 4260 millions , , 4260 . Hence- - = 486and/ = - millions, I 486 which gives V = s /yl = 3-2-2 x 4260 486 millions = /Ir^ x 1000 = 1000 V or V= 17,000 feet per second nearly. As in the case of water and iron, so, in general, it may be stated that sound travels faster in liquids than in air, and still faster in solids, the ratio - being least in gases P and greatest in solids. 26. Biot, about 50 years ago, availed himself of the great difference in the velocity of the propagation of sound through metals and through air, to determine the ratio of the one velocity to the other. A bell placed near one ex- tremity of a train of iron pipes forming a joint length of upwards of 3000 feet, being struck at the same instant as the same extremity of the pipe, a person placed at the other extremity heard first the sound of the blow on the pipe, conveyed through the iron, and then, after an interval Experi- mental
terminn
