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Causes influencing the Intensity of Sound.

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as the four bells struck simultaneously. Consequently, for double the distance, the intensity of the sound is only one-fourth. The distance at which sounds can be heard depends on their intensity. The report of a volcano at St. Vincent was heard at Demerara, 300 miles off, and the firing at Waterloo was heard at Dover.

ii. The intensity of the sound increases with the amplitude of the vibrations of the sonorous body. The connection between the intensity of the sound and the amplitude of the vibrations, is readily observed by means of vibrating cords. For if the cords are somewhat long the oscillations are perceptible to the eye, and it is seen that the sound is feebler in proportion as the amplitude of the oscillations decreases.

It is for the same reason that the dying sound of the last blows of a bell become gradually feebler, until they are ultimately extinguished.

iii. The intensity of sound depends on the density of the air in the place in which it is produced. As we have already seen (156), when an alarum moved by clockwork is placed under the bell-jar of the air-pump, the sound becomes weaker in proportion as the air is rarefied.

In hydrogen, which is about 4th the density of air, sounds are much feebler, although the pressure is the same. In carbonic acid, on the contrary, which is half as heavy again as air, sounds are more intense. On high mountains, where the air is much rarefied, it is necessary to speak with some effort in order to be heard, and the discharge of a gun produces only a feeble sound. During a severe frost, sounds are heard at a greater distance, because air is then more dense and more homogeneous; and country people will often predict the weather from the sound of the village bell. For the sound is modified by the presence of moisture, which alters the elasticity and the density.

iv. The intensity of sound is modified by the motion of the atmosphere and the direction of the wind. In calm weather sound is always better propagated than when there is wind; in the latter case, for an equal distance, sound is more intense in the direction of the wind than in the contrary direction.

v. Lastly, sound is strengthened by the proximity of a sonorous body. A string made to vibrate in free air and not near a sounding body has but a very feeble sound; but when it vibrates above a sounding-box, as in the case of the violin, guitar, or violoncello,

its sound is much more intense. This arises from the fact that the box and the air which it contains vibrate in unison with the string. Hence the use of sounding-boxes in stringed instruments.

163. Influence of tubes on the transmission of sound. The diminution in the intensity of sound with the distance is due to the fact, that the sound waves are propagated in the form of continually increasing spheres; and it may indeed be proved geometrically, that since sound is thus transmitted, its intensity must be inversely as the square of the distance. If, however, the sound is sent through a long tube, the waves are propagated in only one direction, and sound can be transmitted to great distances without appreciable alteration. M. Biot found that in one of the Paris water pipes, 1,040 yards long, the voice lost so little of its intensity, that a conversation could be kept up at the ends of the tube in a very low tone; so much so, that in order not to be heard, it was necessary, as Biot expressed it, not to speak at all. The weak

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ening of sound becomes, however, perceptible in tubes of large diameter, or where the sides are rough.

This property of transmitting sounds was first applied in England for speaking tubes, which are used in hotels and large estab

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Speaking Trumpet.

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lishments for transmitting orders. They consist of caoutchouc tubes of small diameter, provided at each end with an ivory or bone mouthpiece, and passing from one room to another. If a person speaks at one end of the tube, he is distinctly heard by a person applying his ear (fig. 140) at the other end.

One of the most important applications of acoustical principles is the Stethoscope. It consists of a cylinder of hard wood about a foot long and 1 inch broad at one end, and in which a longitudinal passage is bored. One end of the stethoscope is held against the diseased part of the body, and the ear is held against the other. The practised physician can detect the existence of internal cavities by the peculiar sound emitted, and which is strengthened by resonance.

164. Speaking trumpet.-These instruments are based both on the reflection of sound, and on its conductibility in tubes. The speaking trumpet, as its name implies, is used to render

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the voice audible at great distances.

It consists of a slightly 'conical tin or brass tube (fig. 141), very much wider at one end (which is called the bell), and provided with a mouthpiece at the other. The larger the dimensions of this instrument the greater is the distance at which the voice is heard. Its action is usually ascribed to the successive reflections of sonorous waves from the

sides of the tube, by which the waves tend more and more to pass in a direction parallel to the axis of the instrument. By means of the speaking trumpet, the word of command can be heard on board ship above the noise of the waves.

165. 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 metallic tube, one of whose extremities, terminating in a bell, receives the sound, while the other end is introduced into the ear (fig. 142). This instrument is the reverse

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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 developed, are concentrated on the auditory apparatus, and produce a far greater effect than divergent waves would have done.

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

-167] Characteristics of Musical Sounds.

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CHAPTER II.

MUSICAL SOUND. PHYSICAL THEORY OF MUSIC.

165a. Difference between musical sound and noise.- Sounds are distinguished from noises. Sound properly so called, or musical sound, is that which produces a continuous sensation, and the musical value of which can be determined: while 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, or the noise of the waves. Nevertheless, the difference between sound and noise is 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.

166. Characteristics of musical sounds.-Musical 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 per 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 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.

167. 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. By the aid of apparatus which he invented, he ascertained that the deepest sounds are produced

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