ACOUSTICS. 70 
time the maximum of their velocity, and likewise reach simultaneously the 
terminus of their path, again to recommence in an inverted order. In 
standing wave vibrations of this character, the air is condensed uniformly in 
the tube when the single strata of air pass their position of equilibrium with 
the maximum of their velocity: if the particles have arrived at the extreme 
points of their course in their oscillation towards the closed end of the tube, 
the greatest condensation here takes place. If, now, they begin to return 
after half an undulation, a rarefaction takes place at the closed end of the 
tube; at the open end there is neither a marked condensation nor rarefac- 
tion. When the tube has an opening in any part of its length, the formation 
of a standing wave experiences an interruption, since in the moment of 
greatest condensation the air can escape, and can enter during the rarefac- 
tion ; this circumstance operates less as the aperture is nearer the open end, 
since here neither the condensation nor the rarefaction is so great as to 
exercise any material influence. Cutting off the tube at this place would 
produce the same effect. and the sound waves would thus be no longer than 
from the beginning of the tube to the orifice. — 
The formation of a standing air wave depends, then, upon the relation 
between the length of the tube and the wave length of the incident tone; it 
is also essential to the formation of a.standing wave in the tube, that close 
to the bottom the amplitude of oscillation shall become almost nothing; that 
there the alternating condensations and rarefactions shall take place, while 
at the open end they must not occur. To this end the distance of the 
opening from the bottom of the tube must be 1, 3, 5, 1, &c., of a wave 
length, and we then obtain in the tube vibration nodes similar to those 
which we have already found to exist in strings and plates. 
To put the air in a closed tube into such vibration, we need only bring 
an oscillating body near the open end of the tube. which shall give such a 
tone that the length of the tube has one of the above proportions (4, 3, &c.) 
to the wave length. If, for example, a vibrating tuning fork be placed 
about two inches above the open extremity of a glass tube closed below, 
then if the latter is of the proper length, the two will become resonant, in 
which case the strata of air contained in the tube will be put into a 
condition of standing vibrations. By this means the tone of the tuning fork 
is increased considerably in intensity. If the tube be too long for the 
sounding body, it may be shortened to the proper length by pouring in 
water. Instead of the tuning fork, one of the glass plates used in the 
production of sound figures, or a glass bell, may be intonated witha fiddle-bow 
before the opening. Savart constructed for this purpose the apparatus 
represented in pl. 19, fig. 92. It consists of two wide tubes, movable one 
within the other by means of a screw, by which the sound tube may be 
lengthened or shortened at pleasure. Before the opening of the tube 
stands a glass bell which can be sounded by means of a fiddle-bow. 
Bringing the tube to the proper length, the sound of the bell will be much 
increased in intensity ; removing the bell from the vicinity of the tube, by 
sliding it along the groove in the base of the apparatus, the tone will 
become remarkably thinner. 
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