Echo (Gr. from a noise), a sound reflected by an opposing surface and repeated to the ear of a listener. The nature of those pulses that are propagated through the air to the ear and produce the sensation of sound is fully explained under the latter title, where also it is shown that the sound pulse is partly reflected when it encounters in its path a medium of different elasticity or density ; if the reflected sound reach the observer so long after the original sound as to constitute a distinct noise, it is called an echo. Simple echoes, and even those that repeat several times in succession the words of the human voice or other sounds, are familiar to all. Of more remarkable cases we may instance the following. A writer in 1766 states that at the Simonetta palace near Milan there was an echo that repeated 60 times the sound of a pistol; this echo does not now exist. Sir John Herschel quotes the case of an echo at Woodstock park that repeats 17 syllables in the daytime and 20 at night. Dr. Page (1839) notices one at Belvi-dere, Allegany co., N. Y., that repeats three syllables distinctly 11 times, the observer standing between two barns.

Most remarkable, however, are the phenomena of harmonic echoes, or those that repeat in a different key the direct sound. Dr. Page observed such an echo in Fairfax co., Va., which repeats 13 syllables three times; and if 20 notes be played on a flute, they are returned with perfect distinctness, but some of them are raised in pitch by a third, a fifth, or an octave, the effects varying with the state of the atmosphere. Tyndall describes the echoes of the Alpine horn rebounding from the rocks of the Wetter-horn or Jungfrau as dying away in successive reflections, gradually becoming more soft and flute-like. Dr. Brewer in his work on " Sound and its Phenomena" (1864) instances the following cases: Not far from Coblentz an echo is found that makes 17 repetitions at unequal intervals, some loud, some soft; some to the right, others to the left of the observer; some in unison with the direct sound, others a third, fifth, or tenth of the fundamental. At the lake of Killarney is an echo that renders an excellent second to any simple air played on the bugle. Some distance from Glasgow there was formerly a remarkable case in which eight or ten notes of a trumpet were repeated a third lower, and again a second and third time, each time lower still.

The Hon. J. W. Strutt, now Lord Rayleigh, observed ("Nature," 1873) the sound of a woman's voice echoed from a plantation of firs, but its pitch raised an octave; with a man's voice the phenomenon could not be produced. - The various interesting peculiarities of echoes depend upon the conditions under which the reflection takes place, and the position of the observer with respect to the reflecting surfaces; these conditions may be so varied as to more or less affect the intensity and the quality of the original sound, and we will separately consider these two peculiarities. The intensity of a sound varies, other things being equal, directly as the solid angle included at the origin of the sound between the extreme limits of the wave that enters the observer's ear. If the reflecting surface be plane and so small that it subtends a smaller angle than the tympanum of the ear, the intensity of the observed echo will be diminished in proportion to the size of the reflector. If the effective surface be larger than this limit, and nothing of intensity be lost in the act of reflection, the echoes will be as loud as the direct sounds that have passed over the same length of path.

There is however always in the act of reflection an actual loss, depending on the relative density and elasticity of the air and the reflecting body; this principle is applied to deaden the echoes within a poorly contrived auditorium, by encasing the bare walls in wooden panels or draping them with any light material. Two planes may be so placed that the reflected sounds proceeding from each reach the observer at the same instant; he will then perceive an echo of twice the intensity of that produced by either reflector separately. The curvature of an elliptical mirror is such that all the rays of sound, or to speak more properly the whole wave of sound, that starts from one focus will be reflected precisely to the other focus, so that the ear placed at this point perceives a sound as intense as that at the origin; this principle is applied in the construction of whispering galleries, where, however, circular or other curved surfaces frequently replace the ellipse. If a sound originate near the focus of a parabolic mirror, the reflected portion of the wave will be confined to a cylindrical or conical space in front of the mirror; a principle that finds application in the construction of speaking trumpets and tubes, ear trumpets, sounding boards for pulpits, etc.

The louder portions of the rolling of artillery or of a clap of thunder are doubtless sometimes the effect of a concentration of several echoes reflected from objects properly placed with respect to the observer. On the other hand, a convex surface scatters the waves of sound and diminishes the intensity of the echo; a principle that finds frequent application in the construction of large halls, whose walls, ceilings, pillars, etc, are covered with protuberant convex ornaments. If the reflecting surfaces are arranged in a promiscuous manner, there will be heard a confused mixture of echoes, each perhaps so faint that the direct sound greatly preponderates; and in the case of many public halls it will be noticed that if empty the speaker's voice is unpleasantly reechoed, while if filled by an audience the echoes become much subdued and often inappreciable. So also a wave of sound passing through a mixture of heterogeneous bodies (such as a forest, currents of hot and cold air, a glass full of champagne, a stratum of rock full of faults and fissures, etc.) is quite completely broken up into smaller pulses moving in every possible direction.

Thus fog bells and whistles, and indeed all other sounds, are heard further during cloudy and foggy weather, and during the night, when the earth is shaded from the sun's heat; and balloonists testify that during the night they hear terrestrial sounds more distinctly. A mixture of rapid currents, even if the liquid be homogeneous, has the same effect; so that the attempts made in 1870 during the siege of Paris to send sound signals through the waters of the Seine were quite unsuccessful, the range of distinct hearing being far less than in the quiet waters of a lake. - The nature of a pulse of sound is such that if two or more pulses meet under certain conditions they will interfere with each other so as to produce silence instead of sound at the point of their intersection. The echoes within rooms of regular symmetrical proportions do thus interfere with each other, and to a slight extent with the direct waves of sound, so that the loudness of the sounds perceived by the ear varies greatly with a change of position of a few feet. In order that reflected waves should thus produce silence, they must have travelled over paths differing in length by some odd multiple (3, 5, 101, etc.) of a half of the wave length peculiar to the pitch of the sound in question.

Because of the variety in the length of the waves that issue from the vocal organs, it follows that a point in an auditorium may be unfavorable to the perception of certain notes in the speaker's voice or in the music of an orchestra, yet favorable to the perception of all others. In the study of the acoustic properties of public halls, Langhans (1810) and Orth (1871) have made valuable investigations. Some of their results are as follows: 1. The phenomena of interference are of minor importance as disturbing elements, while the principal evil to be avoided is the confusion and repetition of echoes. 2. It is less important to provide for the concentration of the sounds of the speaker's voice than for the suppression of all echoes. 3. A difference of path between the direct and the reflected sounds of from 15 to 22 ft. does not disturb and may even assist the hearing; a difference of from 185 to 215 ft. may be disregarded because of the comparative feebleness of the echo; a difference of 30 ft. is to be avoided, as being the most annoying. 4. Low roofs, as in theatres, are advantageous; high ceilings, as in Gothic churches, are of no decided advantage, and may help to produce undesirable echoes. 5. If wood panelling or plaster is introduced to deaden the echo, it is most important to attend to the backing by which the panels are fastened to the walls. - ■ The pitch of an echo, like that of any sound, depends on the rapidity with which the individual pulses encounter the tympanum.

When these pulses follow each other at the rate of from 10 to 16 per second, the ear ceases to be able to separate one from another, and the whole are merged in an apparently continuous humming noise or a musical note of low pitch; the pitch increases directly as the rapidity of the pulsation. If the pulses occur at irregular intervals, and with unequal intensities, a noise or a sense of confusion is produced. These principles find an application in the case of sound reflected from a series of plane reflecting surfaces, such as the palings of a fence, a row of square pillars, etc.; in these cases the original sound does not appear to bo echoed, but instead thereof we hear a musical note, generally of high pitch, lasting for a second or two only, and rapidly diminishing in intensity; if the observer be in motion, the individual echoes reach his ear more or less rapidly than if he be stationary, thus producing a corresponding change in the pitch. Lord Rayleigh has shown that a group of bodies whose dimensions are quite small in comparison with the wave lengths of sound reflect the first harmonic or octave 16 times more powerfully than the fundamental tone; and in general the reflecting or diverting power of ■ small obstacles varies inversely as the fourth power of the wave length.

When therefore a composite note, such as those of the human voice, is echoed back from such a group of objects, the notes of higher pitch will be returned in far greater proportion, and the general effect will be that the echo appears to be pitched in a higher key than the original. On the other hand, the direct wave, being shorn of its higher elements, will appear to be duller than the original, and may appear to have fallen an octave, since it is well known that pure tones are apt to be estimated too low. It is therefore evident that the sounds from any musical instrument, if echoed from a proper group of surfaces, will be shorn of the lower or fundamental tones and appear pitched a third, a fifth, etc, higher, as in the harmonic echoes above enumerated; while on the other hand, if echoed from a plane surface studded with small obstacles, they may bo deprived of those higher rates of vibration that constitute the peculiarities of timbre or quality, and be reduced to their fundamental vibrations, whereby the notes from the various instruments are made to sound more like each other, as in the case quoted above from Tyndall. If, on the other hand, a pure tone be echoed from a sounding board or other elastic surface, there are induced in the latter such subordinate harmonic vibrations as it may be capable of, and these communicated to the air return to the ear along with the fundamental note, thus producing an effect as to quality of tone precisely the reverse of that observed by Tyndall.

Echo #1

Echo, in Greek mythology, an oread nymph, daughter of the earth and air. While Jupiter wantoned with the other nymphs, she detained Juno with endless speech. As soon as Juno understood the device, she changed the nymph into an echo. Thus transformed, Echo withdrew to the banks of the Cephissus, not far from Athens, at the foot of Mt. Pentelicus, and became so desperately in love with Narcissus, son of the river god, that she followed him through the forests, in the chase, to the darkness of grottoes, and to the borders of fountains, and ever repeated in solitary places the name of her beloved. Narcissus disdained her passion; and she retreated into the depths of the woods, and pined away in secret. Only her plaintive voice was always heard in the distance, and it was said that her bones were changed into rocks, and her voice alone remained. She was avenged by Nemesis, who inspired Narcissus with a passion for himself.