ACOUSTICS. $9. 
ACOUSTICS; OR THE THEORY OF SOUND. 
a. General Observations: Wave Motion. 
Before entering upon the theory of sound itself, it will be necessary to 
premise some observations upon the motion of waves in general, as these 
play a great part in this section of Physics. 
Imagine a body making oscillations similar to those of a pendulum, 1n 
which, however, the relative positions of the different parts do not, as in the 
pendulum, remain the same; then these parts, to return to their original 
equilibrium, must likewise take up an oscillatory motion which differs from 
that of the pendulum, in that the mutual position of these particles changes 
every moment. Two conditions of things may here occur: either all the 
parts oscillate at the same instant and in the same time, or the oscillations 
may be propagated in different parts successively, so that one part may 
begin its motion when the preceding has ceased. The first case presents 
itself in a steel spring fastened at one end, or in a string attached at its two 
extremities; in the second case waves are produced, and an illustration 
furnished when a stone is dropped into still: water. All these vibratory 
motions admit of various modifications in extent and rapidity; if they 
exceed a certain degree of velocity, their combined action produces wave 
movements in the surrounding medium, which are propagated to our organs 
of sense, and produce peculiar impressions upon them. These vibrations, 
within certain limits, produce waves in the air, consisting of alternate con- 
densations and rarefactions, and are perceptible to our ears as tones; light 
is the impression which a vastly more rapid vibration of particles produces 
upon our eyes, by inducing wave motions in a peculiar elastic fluid, the 
ether. It will therefore be necessary, as wave motion serves to propagate 
vibrations, to begin with that, and first to consider water waves, whose 
formation and conditions may be directly observed by us. 
If a stone be dropped into water, it forms concentric circular waves, 
which consist of alternate elevations and depressions, in whose advancing 
motion the individual particles of water do not take part, as is shown by the 
fact that a floating body, although rising and falling, yet remains in the 
same place on the water. When regular waves are formed, the single par- 
ticles of water on the surface, during the advance of the wave, describe 
curves returning into themselves, which are only closed when the succeeding 
wave is higher or lower : in cases of great regularity the curves are circles. 
Let us suppose that a motion, assumed to be perfectly regular, is propagated 
from one side to the other over a series of water particles, twelve for 
instance, then, when the first particle has completed its circular motion, the 
twelfth will be just beginning, and each intervening particle will be just 
one twelfth of its course behind the preceding. By means of these different 
motions is produced the curvilineal form of waves, and wave ares are 
formed whose summits are where the water particle has comple‘ed its cir 
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