SUMMARY OF LECTURE II.

A musical sound is produced by sonorous shocks which follow each other at regular intervals, with a sufficient rapidity of succession.

Noise is produced by an irregular succession of sonorous shocks.

A musical sound may be produced by taps which rapidly and regularly succeed each other. The taps of a card against the cogs of a rotating wheel are usually employed to illustrate this point.

A musical sound may also be produced by a succession of puffs. The syren is an instrument by which such puffs are generated.

The pitch of a musical note depends solely on the number of vibrations concerned in its production. The more rapid the vibrations, the higher the pitch.

By means of the syren the rate of vibration of any sounding body may be determined. It is only necessary to render the sound of the syren and that of the body identical in pitch, to maintain both sounds in unison for a certain time, and to ascertain, by means of the counter of the syren, how many puffs have issued from the instrument in that time. This number expresses the number of vibrations executed by the sounding body.

When a body capable of emitting a musical sound-a tuning-fork for example-vibrates, it moulds the surrounding air into sonorous waves, each of which consists of a condensation and a rarefaction.

The length of the sonorous wave is measured from

condensation to condensation, or from rarefaction to rarefaction.

The wave-length is found by dividing the velocity of sound per second by the number of vibrations executed by the sounding body in a second.

Thus a tuning-fork which vibrates 256 times in a second produces in air of 15° C., where the velocity is 1,120 feet a second, waves 4 feet 4 inches long. While two other forks, vibrating respectively 320 and 384 times a second, generate waves 3 feet 6 inches and 2 feet 11 inches long.

A vibration, as defined in England and Germany, comprises a motion to and fro. It is a complete vibration. In France, on the contrary, a vibration comprises a movement to or fro. The French vibrations are with us semivibrations.

The time required by a particle of air over which a sonorous wave passes, to execute a complete vibration, is that required by the wave to move through a distance equal to its own length.

The higher the temperature of the air, the longer is the sonorous wave corresponding to any particular rate of vibration. Given the wave-length and the rate of vibration, we can readily deduce the temperature of the air.

The human ear is limited in its range of hearing musical sounds. If the vibrations number less than 16 a second, we are conscious only of the separate shocks. If they exceed 38,000 a second, the consciousness of sound ceases altogether. The range of the best ear covers about 11 octaves, but an auditory range limited to 6 or 7 octaves is not uncommon.

The sounds available in music are produced by vibrations comprised between the limits of 40 and 4,000 a second. They embrace 7 octaves.

The

range

of the ear far transcends that of the eye,' which hardly exceeds an octave.

By means of the Eustachian tube, which is opened in the act of swallowing, the pressure of the air on both sides of the tympanic membrane is equalised.

By either condensing or rarefying the air behind the tympanic membrane, deafness to sounds of low pitch may be produced.

On the approach of a railway train the pitch of the whistle is higher, on the retreat of the train the pitch is lower, than if the train were at rest.

Musical sounds are transmitted by liquids and solids. Such sounds may be transferred from one room to another; from the ground-floor to the garret of a house of many stories, for example, the sound being unheard in the rooms intervening between both, and rendered audible only when the vibrations are communicated to a suitable sound-board.

LECTURE III.

VIBRATIONS OF STRINGS HOW EMPLOYED IN MUSIC- INFLUENCE OF SOUND-BOARDS-LAWS OF VIBRATING STRINGS ILLUSTRATIONS ON A LARGE SCALE-COMBINATION OF DIRECT AND REFLECTED PULSES-STATIONARY AND PROGRESSIVE WAVES-NODES AND VENTRAL SEGMENTSAPPLICATION OF RESULTS TO THE VIBRATIONS OF MUSICAL STRINGSEXPERIMENTS OF M. MELDE-STRINGS SET IN VIBRATION BY TUNINGFORKS LAWS OF VIBRATION THUS DEMONSTRATED -HARMONIC TONES OF STRINGS-DEFINITIONS OF TIMBRE OR QUALITY, OF OVERTONES AND CLANG-ABOLITION OF SPECIAL HARMONICS-CONDITIONS WHICH AFFECT THE INTENSITY OF THE HARMONIC TONES OPTICAL EXAMINATION OF THE VIBRATIONS OF A PIANO-WIRE.

WE

E have to begin our studies to-day with the vibrations of strings, or wires; to learn how bodies of this form are rendered available as sources of musical sounds, and to investigate the laws of their vibrations.

To enable a string to vibrate transversely, it must be stretched between two rigid points. Before you, fig 29, is

VIBRATIONS OF STRINGS.

87

an instrument employed to stretch strings, so as to render their vibrations audible. From the pin p, to which one end of it is firmly attached, the string passes across the two bridges B and B', being afterwards carried over the wheel H, which moves with great freedom. The string is finally stretched by a weight w of 28 lbs. attached to its extremity. The bridges B and B', which constitute the real ends of the string, are fastened on the long wooden box M N. The whole instrument is called a monochord or sonometer.

I take hold of the stretched string BB' at its middle point, pull it aside, and liberate it suddenly. Let us henceforth call this act plucking the string. After having been plucked, the string springs back to its first position, passes it, returns, and thus vibrates for a time to and fro across its position of equilibrium. You hear a sound, and I at the same time can plainly see the limits between which the string vibrates. The sonorous waves which at present strike your ears do not proceed immediately from the string. The amount of motion which so thin a body imparts to the air is too small to be sensible at any distance. But the string is drawn tightly over the two bridges BB'; and when it vibrates, its tremors are communicated through these bridges to the entire mass of the box M N, and to the air within the box, which thus become the real sounding bodies.

That the vibrations of the string alone are not sufficient to produce the sound, may be thus experimentally demonstrated :—A B, fig. 30, is a piece of wood placed across an iron bracket c. From each end of the piece of wood depends a rope ending in a loop, while stretching across from loop to loop is an iron bar m n. From the middle of the iron bar hangs a steel wire ss', stretched by a weight w of 28 lbs. By this arrangement, the wire is detached from all large surfaces to which it could impart its vibrations. Here is a second wire t t, fig. 31, of the