CHAMBERS'S INFORMATION FOR THE PEOPLE. 



is also a lower limit below which grave sounds 

 cannot be heard, and although these limits will be 

 different for different ears, still, for the average ear, 

 only those sounds are audible which are made by 

 more than 32, and less than 72,000 vibrations per 

 second. 



Like waves of light, sound-waves can be re- 

 flected by plane and curved surfaces, and also re- 

 fracted by suitable lenses. When the sound-waves 

 are reflected by a plane surface, such as a smooth 

 wall or the flat face of a rock, an echo is produced, 

 if the reflecting surface be at a sufficiently great 

 distance. The necessity for this proviso may be 

 thus shewn. However short a time a sound may 

 last, the impression it produces on the ear remains 

 a perceptible time, which is about the tenth of a 

 second ; so that, if two sounds follow each other in 

 less than the tenth of a second, they interfere with 

 each other. In the tenth of a second, sound will 

 travel, at ordinary temperatures of the air, about 

 in feet ; and if the reflecting wall be less than 55? 

 feet distant from the point whence the sound pro- 

 ceeds, there will be less than the tenth of a second 

 between the time of the original sound leaving the 

 point, and the reflected sound returning to it, and 

 a confusion of sounds is produced with no echo. 

 It is this confusion of sounds that interferes with 

 hearing in churches, lecture-rooms, and other large 

 buildings that are not built on acoustical prin- 

 ciples. A partial remedy for the defect consists 

 in weakening the reflection by destroying the even- 

 ness of the surface, as by suspending curtains at 

 intervals along the walls. If the wall is exactly 

 55i feet distant, there is just sufficient time be- 

 tween the production of the sound and the arrival 

 of the echo for the ear to discriminate them as 

 two separate sounds, so that an echo cannot be 

 distinctly heard unless the reflecting surface be at 

 a distance not less than 55^ feet The number of 

 syllables that an echo can repeat is the number 

 that can be pronounced in the time that sound takes 

 to travel to and from the reflecting surface. The 

 celebrated echo at the tomb of Metella, wife of 

 Crassus, near Rome, was said to have repeated 

 distinctly the first line of the ^Eneid, which con- 

 tains fifteen syllables. If we allow three seconds 

 as the time necessary to repeat this line distinctly, 

 the reflecting surface must have been at a distance 

 of 1668 feet. If the sound, after being once re- 

 flected, is reflected a second time, a double echo 

 is produced ; and if the reflecting surfaces be many, 

 there is a multiple echo. One of the most interest- 

 ing echoes of this kind is that which occurs on the 

 banks of the Rhine, at the Lorlei rocks. If the 

 weather be favourable, the report of a pistol fired on 

 one side is repeated from crag to crag on opposite 

 sides of the river alternately, for as many as ten or 

 twelve times. At the chateau of Simonetta, in 

 Italy, an echo between two parallel wings of the 

 building repeats a sound thirty times. In whisper- 

 ing-galleries, a feeble sound made at one par- 

 ticular part of the building is repeatedly reflected 

 from the smooth walls, and many of the reflected 

 waves finally converge to another point where the 

 sound is distinctly heard. In the dome of St 

 Paul's Cathedral in London, a whisper at one side 

 is heard at the other, though at all intermediate 

 places it is quite inaudible. 



That the sound-waves are refracted in passing 

 obliquely through a medium denser than air, is 

 clearly proved by the following experiment, first 



Fig. 32- 



performed by M. Sondhauss. AB is a double con- 

 vex bag, formed 

 of collodion, 

 and filled with 

 carbonic acid 

 gas, which is 

 rather more than 

 one and a half 

 times heavier 

 than air. A 

 watch, W, is 

 placed in the axis of the gas-lens, and the ear, E, of 

 the observer is shifted backwards and forwards 

 also in the axis of the lens, and it is found that there 

 is one point, E, where the ticking of the watch is 

 distinctly heard ; though nearer and further from 

 the lens, the sound is scarcely heard. E and W 

 are therefore conjugate foci of the gas-lens, and 

 the sound-waves have been refracted by the lens 

 exactly as the light-waves in travelling through a 

 glass lens. 



THEORY OF THE MUSICAL SCALE. 



A simple musical tone, as that yielded by a 

 tuning-fork, is produced by a continuous rapid 

 vibration, if the number of single vibrations (the 

 forward and the backward motions being two 

 single, or one double vibration) fall between the 

 limits before stated. One tone may differ from 

 another in pitch, as the tone of one tuning-fork 

 may be higher or lower than that of a second. 

 The pitch, as we have seen, depends on the number 

 of vibrations per second, or, which comes to the 

 same thing, on the length of the wave, for as the 

 velocity of sound is 1112 feet per second, if there 

 are 100 vibrations per second, the wave-length is 

 1 1 '12 feet Again, the same tuning-fork may emit 

 a weak or a loud tone ; or musical tones of the 

 same pitch may differ in intensity ; and the in- 

 tensity has been shewn to vary with the square 

 of the range, or amplitude of vibration. Once 

 more, if a pianoforte be made to yield a tone of 

 the same pitch and intensity as the tone of the 

 tuning-fork, we are conscious of a difference be- 

 tween the two tones, and this is a difference in 

 quality, or colour, so to speak. In French, this 

 difference is called timbre, and in German, klang- 

 farbe (colour-tint). The cause of this difference 

 will be explained presently. 



Let us now take any note of 

 the pianoforte, say C on the 

 annexed scale, which is pro- 

 duced by 528 vibrations in a 

 second, or 480 in the unit of 

 time, if we make our unit 

 of a second. If another note be yielded by 960 

 vibrations in the unit of time, the ear at once 

 recognises an agreeable concordance when the 

 two are sounded together. And similarly for any 

 other two notes whose vibrations are as one to 

 two. If we take two notes between these, such 

 that their vibrations in the same time are to C's 

 as i^ to I and I to I J, we have four notes, which, 

 when sounded together, produce a very pleasing 

 effect, and form what is called a major chord. 

 The lowest three of the chord have their vibrations 

 in the proportion of 4, 5, and 6, and constitute a 

 harmonic triad. Let us form two more triads 

 from this one, by making the highest of the three 

 the lowest of the second triad, and the lowest of 



C = 528 vibrations. 



