Newton was the first who attempted to deduce from mechanical principles the velocity of sound, but only for the particular ease in which each particle of air in the path of the sound is supposed to move backward and forward according to the same law as the bob of a pendulum (q.v.). He showed that this species of motion is consistent with the elastic properties of air, as given by Boyle's or Mariotte's law (q.v.), viz., that the pressure of air is proportional to its density. The velocity of sound in this case is of course to be found from the time which elapses between the commencement of the motion of any one particle of air, and that of another at a given distance from it, in the direction in which the sound is moving. The numerical result deduced by Newton with the then received experimental data for the compressibility of air, was 979 ft. per second. This investigation was very defective, applying, in fact, solely to the special case of a pure musical note, continually propagated without lateral divergence; yet the obtained by Lagrange from a complete analysis of the question, gave precisely the same' mathematical result.
But, by direct measurements, carefully made, by observing at night the interval which elapses between the flash and the report of a cannon at a known distance,. the velocity of sound has been found to be considerably greater—in fact, about 1090 ft. per second, at the temperature of freezing water.
Newton seeks for the cause of the discrepancy between theory and observation in the idea that the size of the particles of air is finite compared with their mutual distance; and that sound is instantaneously propagated through the particles themselves. Thus, sup posing the particles to have a diameter of the distance between them, we must add to the space traveled by sound in a second, i.e., to the velocity—which will thus he brought up to (1 979 ft.=1038 ft. nearly, which is a very close approximation to the actual value given above.
This is not one of Newton's happiest conjectures..—for, independent of the fact that such an assumption would limit definitely the amount of compression which air could undergo, and, besides. is quite inconsistent with the truth of Boyle's law for even mod erate pressures, it would result from it that sound should travel slower in rarefied, and quicker in condensed air. Now, experiment shows that the velocity of sound is unaf fected by the height of the barometer; and, indeed, it is easy to see that this ought to be the case. For in condensed air the pressures arc increased proportionally to the increase of condensation, and the mass of a given bulk of air is increased in the same proportion. Hence, iu a sound-wave in condensed air, the forces and the masses are increased pro portionally, and thus the rate of motion is unaltered. But the temperature of the air has
an effect on sound, since we know that the elastic force is increased by heat, even when the density is not diminished; and therefore the velocity of sound increases with the temperature at the rate of about 41 ft. per Fahr. degree, as is found by experiment.
Newton's explanation of the discrepancy between theory and experiment being thus set aside, various suggestions were made to account for it; some, among whom was Euler, imagining that the mathematical methods employed, being only approximate, in volved a serious error.
The explanation was finally given by Laplace, and is simple and satisfactory. When air is suddenly compressed (as it is by the passage of a sound-wave), it is heated; when suddenly rarefied it is cooled, and this effect is large enough to introduce a serious modi fication into the mathematical investigations. The effect is in either case to increase the forces at work—for, when compressed, and consequently heated, the pressure is greater than that due to the mere compression—and, when rarefied, and consequently cooled, the pressure is diminished by more than the amount dne to the mere rarefaction. When this source of error is removed, the mathematical investigation gives a result as nearly agree ing with that of observation as is consistent with the unavoidable errors of all experi menta•data. It is to be observed that, in noticing this investigation, nothing has been said as to the pitch or quality of the sound, for these haVe nothing to do with the velocity. It must, however, be remarked here that, in the mathematical investigation, the compres sions and rarefactions are assumed to be very small; i.e., the sound is supposed to be of moderate intensity. It does not follow, therefore, that very violent sounds have the same velocity as moderate ones, and many curious observations made during thunder storms seem to show that such violent sounds are propagated with a greatly increased ve locity. (See a paper by Earushaw in the Phil. Mag. for 1861.) It is recorded that in one of Parry's arctic voyages, during gun-practice, the officer's command 'Fire' was heard at great distances across the ice 'after the report of the gun.
Since sound consists in a wave-propagation, we should expect to find it exhibit all the ordinary phenomena of waves (q.v.). Thus, for instance, it is reflected (see Folio) ac cording to the snipe law as light. It is refracted in passing from one medium to another of different density or elasticity. This has been proved by concentrating in a focus the feeble sound of the ticking of a watch. and rendering it audible at a considerable dis tance, by means of a lens of collodion filled with carbonic acid gas.