Velocity of Sound in various Solids.

and heard at the other, the interval between the arrival of the sound through the air and through the iron was noted. The length being known, the time required for the transmission of the aerial sound became known with great precision, and thence the time of transmission through the iron became known also. The mean result of their observations was 11090 feet per second for the velocity of sound in cast iron at the temperature of the experiment, or 51°.8 Fahrenheit. This is about 103 times its velocity in air.

c. Chladni assigns 11802 feet for the velocity of sound in brass. Laplace, calculating on an experiment of Borda, on the compressibility of brass, makes it 11682 feet.

=

According to Chladni, the following are the velocities of sound in different solids, that in air being taken for unity: tin = 73, silver 9, copper = 12, iron = 17, glass = 17, baked clay = 10 to 12, wood of various species = 11 to 17. The error in the case of iron throws a doubt on all the rest; unless, perhaps, steel be meant.

43. The force of a pull, push, or blow must be transmitted, by an iron bar or chain, with the same velocity as sound. For every 11090 feet of distance, it will, then, reach its point of action one second after the moment of its emanation from the first mover.

In all moderate distances, then, the interval is utterly insensible. But were the sun and the earth connected by an iron bar, no less than 1074 days, or nearly three years, must elapse before a force applied at the sun could reach the earth. The force actually exerted by their mutual gravity may be proved to require no appreciable time for its transmission. How wonderful is this connection !

Divergence of Sound from the End of a Pipe.

CHAPTER VI.

THE DIVERGENCE AND DECAY OF SOUND.

44. HITHERTO we have taken no account of the lateral divergence of sound, which we have supposed confined by a pipe; but it is evident that condensation taking place in any section of such a channel will urge the contained air laterally against the side of the pipe, as well as forward along its axis; and, consequently, if the pipe were cut off at any point, the sound would diverge from that point into the surrounding air. Accordingly, when any one speaks through a long straight tube the voice is heard laterally, as if proceeding from the mouth of the speaker at the orifice.

45. Sounds excited in, or impulses communicated to, any portion of the air or other elastic medium, spread, more or less perfectly, in all directions, in space.

a. We say more or less perfectly; for though there are sounds, as the blow of a hammer, the explosion of gunpowder, &c. which spread equally in all directions, yet there are others which are far from being in that predicament.

For instance, a common tuning-fork (a piece of steel in the shape represented in fig. 6.) being struck sharply, when held by the handle (4) against a substance, is set in vibration, the two branches of the fork alternately approaching to and receding from each other. Each of them, consequently, sets the air in vibration, and a musical tone is produced. But this sound is very unequally

Unequal Divergence of certain Sounds.

audible in different directions. If the axis of the fork, or the line to which it is symmetrical, be held upright about a foot from the ear, and if it be turned round this axis while vibrating, at every quarter revolution the sound will become so faint as scarcely to be heard, while in the intermediate arcs of rotation it is heard clear and strong. The audible situations lie in lines perpendicular and parallel to the flat faces of the fork, the inaudible at 45° inclined to them. This elegant experiment, due originally to Dr. Young, has recently been called into notice by Weber.

b. The non-uniformity of the divergent pulses, which constitute certain sounds, is easily demonstrated by considering what happens when a small disc is moved to and fro in a line perpendicular to its surface. The aerial molecules in front of the disc are necessarily in an opposite state of motion from those similarly situated behind it. Hence, if we conceive a wave propagated spherically all around it, the vertices of the two hemispheres in front and behind are in opposite motions with respect to the centre.

But with regard to that wave of the sphere where the vibrating plate prolonged cuts it, there is evidently no reason why its molecules should approach to or recede from the centre, or, rather, there is as much reason for one as for the other. They will, therefore, either remain at rest, or move tangentially; so that the motion of the whole sounding surface, or wave, will, in this case, be rather as in fig. 7 than in fig. 8; and a corresponding difference, both in the intensity and character of the sound heard in different directions, may be fairly expected.

46. The mathematical theory of such pulses as these is of the utmost complication and difficulty, depending on the integration of partial differential equations with four independent variables, viz., the time and the three coördinates of the moving molecules. It is therefore of much too high a nature to have any place in an essay like the present. We shall merely content ourselves with stating the following, as general results in which mathematicians are agreed.

Case of a Spherical Undulation, alike on all Sides.

1st. The velocity of propagation of a sonorous pulse is the same, whether we regard it as propagated in one, two, or three dimensions, i. e. in a pipe, a lamina, or a mass of air.

2d. Sounds propagated in a free mass of air diminish in intensity, as they recede further from the sonorous centre, and their energy is in the inverse duplicate ratio of this distance, cæteris paribus; or, more generally, they are proportional to the vis viva of the impinging molecules.

a. We shall not attempt a proof of these propositions in the general cases, but content ourselves with illustrating them in one particular but important case, viz. when the initial impulse is confined to a very small space, and consists in any small radiant motion of all the particles of a spherical surface in all directions equally from the centre.

b. Since the initial wave is spherical, and similar in all its parts, it will evidently retain this property as it dilates by the progress of the impulse. If, then, it be conceived to be divided into its infinitesimal elements by a system of pyramidally disposed plane surfaces, having the common vertex in the centre of the sphere, each of these elements will form the base of one of the pyramids, and its molecules will advance and recede along the axis, as the pulse traverses them, without any change of their relative positions, inter se; so that the whole wave may be regarded as broken up into partial waves, each advancing as if confined within a pyramidal pipe, independently of all the rest.

c. Now in any one of these imaginary pipes. the pulse will be propagated from layer to layer of the included particles, with the same velocity as if the pipe were cylindrical. For the divergence of the sides of the pipe can only cause a lateral extension, and thence a diminished thickness of the stratum, and will, therefore, alter the velocity of each molecule and the extent and law of mo

PART II.

MUSICAL SOUNDS.

CHAPTER I.

THE NATURE AND PRODUCTION OF MUSICAL SOUNDS.

47. EVERY impulse mechanically communicated to the air, or other sonorous medium, is propagated onward by its elasticity, as a wave or pulse; but, in order that it shall affect the ear, as an audible sound, a certain force and suddenness is necessary.

The slow waving of the hand through the air is noiseless, but the sudden displacement and collapse of a portion of that medium by the lash of a whip produces the effect of an explosion. It is evident that the impression conveyed to the ear will depend entirely on the nature and law of the original impulse, which being completely arbitrary, both in duration, violence, and character, will account for all the variety we observe in the continuance, loudness, and quality of sounds. The auditory nerves, by a delicacy of mechanism, of which we can form no conception, appear capable of analyzing every pulsation of the air, and appreciating immediately the law of motion of the particles in contact with the ear. Hence all the qualities we distinguish in sounds — grave or acute, smooth, harsh, mellow, and all the nameless and fleeting peculiarities, which constitute the differences between the tones of different musical instruments-bells, flutes, cords, &c., and between the voices of different individuals or different animals.