Page:Encyclopædia Britannica, Ninth Edition, v. 1.djvu/123

38.As a luminous object may give a succession of images when placed between two or more reflecting surfaces, so also in like circumstances may a sound suffer repetition.

Fig. 9.

To these principles are easily traceable all the peculiarities of echoes. A wall or steep cliff may thus send back, somewhat reduced in intensity, a shout, the report of a pistol, &c. The time which elapses between the sound and its echo may be easily deduced from the known velocity of sound in air, if the distance of the wall be given. Thus, for a distance of $37$ yards, the interval will be found by dividing the double of that or $74$ yard by $370$ yards, the velocity of sound at $50^{\circ }$ Fahr., to amount to ${\tfrac {1}{5}}$ of a second. Hence, if we assume that the rate at which syllables can be distinctly uttered is five per second, the wall must be at a distance exceeding $37$ yards to allow of the echo of a word of one syllable reaching the ear after the word has been uttered, $74$ yards for a word of two syllables, and so on.

If the reflecting surface consists of one or more walls, cliffs, &c., forming together a near approach in shape to that of a prolate spheroid or of a double parabolic surface, then two points may be found, at one of which if a source of sound be placed, there will be produced, by convergence, a distinct echo at the other. As examples of this may be mentioned the whispering gallery in St Paul's, London, and the still more remarkable case of the Cathedral of Girgenti in Sicily mentioned by Sir John Herschel.

39.On similar principles of repeated reflexion may be explained the well-known fact that sounds may be conveyed to great distances with remarkably slight loss of intensity, on a level piece of ground or smooth sheet of water or ice, and still more so in pipes, chimneys, tunnels, &c. Thus, in one of Captain Parry's Polar expeditions, a conversation was on one occasion carried on, at a distance of $1{\tfrac {1}{4}}$ mile, between two individuals separated by a frozen sheet of water. M. Biot heard distinctly from one end of the train of pipes ${\tfrac {3}{5}}$ of a mile long, previously referred to, a low whisper proceeding from the opposite end.

Practical illustrations are afforded by the system of communication by means of tubing now so extensively adopted in public and private buildings, and by the speaking trumpet and the ear trumpet.

40.The prolonged roll of thunder, with its manifold varieties, is partly to be ascribed to reflexion by mountains, clouds, &c.; but is mainly accounted for on a different acoustic principle, viz., the comparatively low rate of transmission of sound through air, as was first shown by Dr Hooke at the close of the 17th century. The explanation will be more easily understood by adverting to the case of a volley fired by a long line of troops. A person situated at a point in that line produced, will first it is evident hear the report of the nearest musket, followed by that of the one following, and so down to the last one in the line, which will close the prolonged roll thus reaching his ear; and as each single report will appear to him less intense according as it proceeds from a greater distance, the roll of musketry thus heard will be one of gradually decreasing loudness. But if he were to place himself at a relatively great distance right opposite to the centre of the line, the separate reports from each of the two wings would reach him nearly at the same moment, and hence the sound of the volley would now approach more nearly to that of a single loud crash. If the line of soldiers formed an arc of a circle having its centre in his position, then the distances gone over by the separate reports being equal, they would reach his ear at the same absolute instant of time, and wit exactly equal intensities; and the effect produced would be strictly the same as that of a single explosion, equal in violence to the sum of all the separate discharges, occurring at the same distance. It is easy to see that, by varying the form of the line of troops and the position of the observer, the sonorous effect will be diversified to any extent desired. If then we keep in view the great diversity of form exhibited by lightning-flashes, which may be regarded as being lines, at the points of which are generated explosions at the same instant of time, and the variety of distance and relative position at which the observer may be placed, we shall feel no difficulty in accounting for all those acoustic phenomena of thunder to which Hooke's theory is applicable.

Part IV.
The Principles of Musical Harmony.

41.A few words on the subject of musical harmony must be introduced here for the immediate purposes of this article, further details being reserved for the special article on that subject.

Sounds in general exhibit three different qualities, so far as their effect on the ear is concerned, viz., loudness, pitch, and timbre.

Loudness depends, cæt. par., on the violence with which the vibrating portions of the ear are excited; and therefore on the extent or amplitude of the vibrations of the body whence the sound proceeds. Hence, after a bell has been struck, its effect on the ear gradually diminishes as its vibrations, loudness or intensity is measured by the vis-viva of the vibrating particles, and is consequently proportional to the square of their maximum velocity or to the square of their maximum displacement. Helmholtz, however, in his remarkable work on the perception of tine, observes that notes differing in pitch differ also in loudness, where their vis-viva is the same, the higher note always exhibiting the greater intensity.

42.Difference of pitch is that which finds expression in the common terms applied to notes: Acute, shrill, high, sharp, grave, deep, low, flat. We will point out presently in what manner it is established that this quality of sound depends on the rapidity of vibration of the particles of air in contact with the external parts of the ear. The pitch of a note is higher in proportion to the number of vibrations of the air corresponding to it, in a given time, such as one second. If $n$ denote this number, then, by § 13, $n={\tfrac {\text{V}}{\lambda }}$, and hence, ${\text{V}}$ being constant, the pitch is higher the less the length $\lambda$ of the wave.

43.Timbre, or, as it is termed by German authors, klang-farbe, rendered by Tyndall into clang-colour or clang-tint, but for which we would substitute the expression acoustic colour, denotes that peculiarity of impression produced on the ear by sounds otherwise, in pitch, loudness, &c., alike, whereby they are recognisable as different from each other. Thus human voices are readily interdistinguishable; so are notes of the same pitch and intensity, produced by different instruments. The question whence arises this distinction must be deferred for the present.

44.Besides the three qualities above mentioned, there exists another point in which sounds may be distinguished among each other, and which, though perhaps reducible to difference of timbre, requires some special remarks, viz., that by which sounds are characterised, either as noises or as musical notes. A musical note is the result of regular,