882. Reflection of Sound.-When sonorous waves meet a fixed obstacle they are reflected, and the two sets of waves-one direct, and the other reflected-are propagated just as if they came from two separate sources. If the reflecting surface is plane, waves di

verging from any centre O (Fig. 608) in front of it are reflected so as to diverge from a centre O' symmetrically situated behind it, and an ear at any point M in front hears the reflected sound as if it came from O'.

The direction from which a sound appears to the hearer to proceed is determined by the direction along which the sonorous pulses are propagated, and is always normal to the waves. A normal to a set of sound-waves may therefore conveniently be called a ray of sound. OI is a direct ray, and I M the corresponding reflected ray; and it is obvious, from the symmetrical position of the points O O', that these two rays are equally inclined to the surface, or the angles of incidence and reflection are equal.

a

Fig. 609.-Reflection from Elliptic Roof.

883. Illustrations of Reflection of Sound.-The reflection of sonorous waves explains some well-known phenomena. If aba (Fig. 609) be an elliptic dome or arch, a sound emitted from either of the foci ff will be reflected from the elliptic surface in such a direction as to pass through the other focus. A sound emitted from either focus

REFLECTION OF SOUND.

887

may thus be distinctly heard at the other, even when quite inaudible at nearer points. This is a consequence of the property, that lines drawn to any point on an ellipse from the two foci are equally inclined to the curve.

The experiment of the conjugate mirrors (§ 468) is also applicable to sound. Let a watch be hung in the focus of one of them (Fig. 610),

and let a person hold his ear at the focus of the other; or still better, to avoid intercepting the sound before it falls on the second mirror, let him employ an ear-trumpet, holding its further end at the focus. He will distinctly hear the ticking, even when the mirrors are many yards apart.1

884. Echo.-Echo is the most familiar instance of the reflection of sound. In order to hear the echo of one's own voice, there must be a distant body capable of reflecting sound directly back, and the number of syllables that an echo will repeat is proportional to the

1 Sondhaus has shown that sound, like light, is capable of being refracted. A spherical balloon of collodion, filled with carbonic acid gas, acts as a sound-lens. If a watch be hung at some distance from it on one side, an ear held at the conjugate focus on the other side will hear the ticking. See also a later section on "Curved Rays of Sound" in the chapter on the "Wave Theory of Light."

distance of this obstacle. The sounds reflected to the speaker have travelled first over the distance OA (Fig. 611) from him to the reflecting body, and then back from A to O. Supposing five syllables to be pronounced in a second, and taking the velocity of sound as 1100 feet per second, a distance of 550 feet from the speaker to the reflecting body would enable the speaker to complete the fifth syllable before the return of the first; this is at the rate of 110 feet

per syllable. At distances less than about 100 feet there is not time for the distinct reflection of a single syllable; but the reflected sound mingles with the voice of the speaker. This is particularly observable under vaulted roofs.

Multiple echoes are not uncommon. They are due, in some cases, to independent reflections from obstacles at different distances; in others, to reflections of reflections. A position exactly midway between two parallel walls, at a sufficient distance apart, is favourable for the observance of this latter phenomenon. One of the most frequently cited instances of multiple echoes is that of the old palace of Simonetta, near Milan, which forms three sides of a quadrangle. According to Kircher, it repeats forty times.

885. Speaking and Hearing Trumpets.-The complete explanation of the action of these instruments presents considerable difficulty. The speaking-trumpet (Fig. 612) consists of a long tube (sometimes 6 feet long), slightly tapering towards the speaker, furnished at this end with a hollow mouth-piece, which nearly fits the lips, and at

SPEAKING AND HEARING TRUMPETS.

889

the other with a funnel-shaped enlargement, called the bell, opening out to a width of about a foot. It is much used at sea, and is found very effectual in making the voice heard at a distance. The explanation usually given of its action is, that the slightly conical form of the long tube produces a series of reflections in directions more and more nearly parallel to the axis; but this explanation fails to account for the utility of the bell, which experience has shown to be considerable. It appears from a theoretical investigation by Lord Rayleigh that the speaking-trumpet causes a greater total quantity of sonorous energy to be produced from the same expenditure of breath.1

Ear-trumpets have various forms, as represented in Fig. 613; having little in common, except that the external opening or bell is much larger than the end which is introduced into the ear. Membranes of goldbeaters' skin are sometimes stretched across their interior, in the positions indicated by the dotted lines in Nos. 4 and 5. No. 6 consists simply of a bell with such a membrane stretched across its outer end, while its inner end communicates with the ear by an indianrubber tube with an ivory end-piece. These light membranes are peculiarly susceptible of impression from aerial vibrations. In Regnault's experiments above

cited, it was found that membranes were affected at distances greater than those at which sound was heard. 886. Interference of Sonor

ous

Undulations.- When two systems of waves are traversing the same matter, the actual motion of each particle of the matter is the resultant of the motions due to each system separately. When these

5

2

Fig. 613. -Ear-trumpets.

Fig. 612. Speaking-trumpet.

component motions are in the same direction the resultant is their

1 Theory of Sound, vol. ii. p. 102.

sum; when they are in opposite directions it is their difference; and if they are equal, as well as opposite, it is zero. Very remarkable phenomena are thus produced when the two undulations have the same, or nearly the same wave-length; and the action which occurs in this case is called interference.

When two sonorous undulations of exactly equal wave-length and amplitude are traversing the same matter in the same direction, their phases must either be the same, or must everywhere differ by the same amount. If they are the same, the amplitude of vibration for each particle will be double of that due to either undulation separately. If they are opposite-in other words, if one undulation be half a wave-length in advance of the other-the motions which they would separately produce in any particle are equal and oppcsite, and the particle will accordingly remain at rest. Two sounds will thus, by their conjoint action, produce silence.

In order that the extinction of sound may be complete, the rarefied portions of each set of waves must be the exact counterparts of the condensed portions of the other set, a condition which can only be approximately attained in practice.

The following experiment, due to M. Desains, affords a very direct illustration of the principle of interference. The bottom of a wooden box is pierced with an opening, in which a powerful whistle fits. The top of the box has two larger openings symmetrically placed with respect to the lower one. The inside of the box is lined with felt, to prevent the vibrations from being communicated to the box, and to weaken internal reflection. When the whistle is sounded, if a membrane, with sand strewn on it, is held in various positions in the vertical plane which bisects, at right angles, the line joining the two openings, the sand will be agitated, and will arrange itself in nodal lines. But if it is carried out of this plane, positions will be found, at equal distances on both sides of it, at which the agitation is scarcely perceptible. If, when the membrane is in one of these positions, we close one of the two openings, the sand is again agitated, clearly showing that the previous absence of agitation was due to the interference of the undulations proceeding from the two orifices. In this experiment the proof is presented to the eye. In the following experiment, which is due to M. Lissajous, it is presented to the ear. A circular plate, supported like the plate in Fig. 594, is made to vibrate in sectors separated by radial nodes. The number of sectors will always be even, and adjacent sectors will vibrate