-172]

Ear-Trumpet.

173

The

can be heard on board ship above the noise of the waves. longer the trumpet the greater the distance to which sound is

carried. A strong man's voice sent through a trumpet 20 feet in length has been heard at a distance of three miles.

172. Ear-trumpet.-The ear-trumpet is used by persons who are hard of hearing. It is essentially an inverted speaking-trumpet, and consists of a conical metal tube, one of whose ends, terminating in a bell, receives the sound, while the other end is introduced into the ear (fig. 156). The action of this instrument is the reverse of

Fig. 156.

that of the speaking-trumpet. The bell serves as mouthpiece; that is, it receives the sounds coming from the mouth of the person who speaks. These sounds are transmitted by a series of reflections to the interior of the trumpet, so that the waves, which would become greatly dispersed, are concentrated on the hearing

apparatus, and produce a far greater effect than divergent waves would have done.

In man and many animals the outer ear is a trumpet which receives the waves of sound. In some animals this part of the hearing apparatus is long and flexible, so that, by adjusting it, the animal can easily recognise the direction from which the sound proceeds.

-174] Characteristics of Musical Sounds.

175

CHAPTER II.

MUSICAL SOUNDS. PHYSICAL THEORY OF MUSIC.

173. Difference between musical sounds and noise.—Sounds are distinguished from noises. Sound properly so called, or musical sound, is that which produces a continuous and regular sensation, and the rate of whose vibrations can be determined. The only condition necessary for producing a musical sound is that the individual impulses shall succeed each other with sufficient rapidity at equal intervals of time. Whatever be its origin, whether it be the ticks of a watch or the puffs of a locomotive, if this condition be fulfilled, the coalescence of the separate impressions produces a musical sound.

On the other hand, noise is either a sound of too short a duration to be determined, like the report of a cannon, or else it is a confused mixture of many discordant sounds, like the rolling of thunder, the rattling of a box of nails, or the noise of the waves. The difference between sound and noise is, however, by no means precise. Savart has shown that there are relations of height in the case of noise, as well as in that of sound, and there are said to be certain ears sufficiently well organised to determine the musical value of the sound produced by a carriage rolling on the pavement.

The action of a noise upon the ear has been compared to that of a flickering light upon the eye; both are painful, in consequence of the sudden and abrupt changes which they produce in their respective nerves.

174. Characteristics of musical sounds.-Musical sounds or tones have three leading qualities, namely pitch, intensity, and timbre or colour.

i. The pitch or height of a musical tone is determined by the number of vibrations in a second yielded by the body producing the tone.

ii. The intensity or loudness of the tone depends on the extent of the vibrations. It is greater when the extent is greater, and less when it is less. It is, in fact, nearly or exactly proportional to the

square of the extent or amplitude of the vibrations which produce

the tone.

iii. The timbre (the French word for 'stamp') is that peculiar quality of tone which distinguishes a note when sounded on one instrument from the same note when sounded on another. Thus when the C of the treble stave is sounded on a violin, and on a flute, the two notes will have the same pitch, that is, are produced by the same number of vibrations per second, and they may have the same intensity, and yet the two tones will have very distinct qualities-that is, their timbre is different (183). By some writers this peculiar property is called the colour.

175. Syren.—The vibrations of any sounding body are so rapid that they cannot be followed by the eye and counted.

Fig. 157.

Various forms of apparatus have been invented for the purpose of determining the number of vibrations corresponding to particular notes. Of these, the one represented in fig. 157 is given as being the simplest and most intelligible. It consists of a circular disc of stout cardboard, or of sheet metal, about a foot in diameter. This disc is perforated by four concentric series of small equidistant holes. For simplicity's sake the inner of these is represented as

having 12, the second 15, the third 18, and the fourth 24 holes ; but a multiple of these ratios, say 48, 60, 72, and 96, is more convenient.

The disc is made to rotate rapidly, and the most convenient plan is to fix it on a turning table (fig. 16), in the place of AB. Then, by means of a glass tube, drawn out at one end so as to be smaller than the diameter of the holes, a current of air is directed against one of the series of holes in the rotating disc. A tone is now heard, which is tolerably pure when the rotations are sufficiently rapid, and the number of vibrations of which can be readily determined. Suppose, for instance, that there are 48 in the inner series of holes. Then each time a hole passes in front of the glass tube a condensed wave is produced which reaches the ear in the ordinary manner. If, for example, the disc makes

-176]

Limit of Perceptible Sounds.

177

16 turns in a second, in each second, 16 times 48, or 768 holes, pass in front of the tube, and there are produced 768 waves, which fall upon the ear within a second, at equal intervals of time. If in like manner the tube were held over the second series of holes, while the rotation goes on at the same rate, we should hear the tones corresponding to 16 times 60, or 960 vibrations in a second. Thus proceeding in like manner, and moving the tube successively from the central to the circumferential series of holes, we hear successively the fundamental note, the major third, the fifth, and the octave (177).

176. Limit of perceptible sounds. Savart, a French physicist, was the first to determine the limit of the number of vibrations which the ear could perceive. He invented an apparatus for this purpose which is known as Savart's toothed wheel (fig. 158). It

consists essentially of a metal wheel, B, with a series of equidistant sharp teeth on its periphery. This is made to rotate at a uniform rate by the motion transmitted by a band, D, from a large wheel, A, and a card, or, still better, a thin elastic steel plate, E, is fixed so that, in the rotation of the wheel, each of the teeth strikes against the plate, and each time produces a sound. If, for instance, the rim of the wheel has 600 teeth, and it is made to rotate 4 times in a second, 2,400 impulses are given in a second. The number of impulses depends thus on the velocity of rotation, and the sounds produced are pure and continuous.

Thus, to determine the number of vibrations corresponding to any particular note, it is simply necessary to turn the wheel at a uniform rate until it produces a note in unison (178) with the one in question. Knowing then the number of teeth on the wheel and

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