ACOUSTICS. 77 
If holes capable of being closed by a slide, are made in different parts of 
an organ pipe, it may be shown that the tone remains unchanged if the 
opening exists at a belly, while another tone is produced if the opening is 
made at a vibration node. 
However little the influence exerted upon the tone of a pipe by the 
direction in which the current of air strikes the mouth-opening, so much 
the more considerable is the effect produced by the shape of the labium, 
and the height of the air-hole. 
The walls including a vibratory mass of air exert a great influence upon 
the tone, and a pipe constructed of poor tin, or of soft or resinous wood, 
gives constantly a smothered feeble tone; even moisture upon the wood 
produces the effect of lowering the tone. 
With regard to the musical notes produced by organ pipes, let us call that 
tone produced by a pipe four feet long, the fundamental note C. If we 
examine the pipes whose tones harmonize with that of C, we shall find that 
the rapidity of oscillation of notes produced by them, stands in a simple 
relation with that of C; the pipes will therefore be 3, 2, 3, , &c., the 
length of C. A pipe of half the length gives then the octave ; that whose 
length is two thirds, and which makes three oscillations to two of C, is the 
fifth; three fourths the length gives the fourth; four fifths of the length 
gives the major third; and five sixths the minor third. The intermediate 
tones are obtained by taking one of the pipes in question as the fundamental 
tone and finding its accord. Thus we obtain for the G accord the fifth D, 
if we take a pipe two thirds the length of G, and the major third Hi with a 
pipe of four fifths, and the minor third B with one of five sixths the length 
of G, &e. 
The deepest tone in music is that C given by a covered pipe of sixteen feet 
in length, or an open one of thirty-two feet. We know, however, that for the 
deepest note of a covered pipe, its wave length must be exactly one fourth 
of the wave length of the tone; in the open air, therefore, the wave length 
of this amounts to 64 feet. Sound travels about 1050 German feet in a 
second, hence it follows that to produce this deepest note there must be 
1050 isda) : 1125 
64. °F 16.4 oscillations in a second (more correctly, perhaps, or 17.5). 
We obtain the number of vibrations necessary to bring out the deepest tone 
of any covered pipe, by dividing 1050 by four times its length. Thus the C’s 
forming the six lower octaves make respectively 16.5, 33, 66, 132, 264, and 528 
vibrations in a second. The greatest number of vibrations observed in a 
second amounts to 24,000; the tone thus produced is, however, scarcely 
audible: the deepest audible tone is that produced by 7.8 vibrations. Still 
higher and deeper tones may perhaps be produced and rendered audible 
by artificial means. 
The length of pipes gives a ready method of determining the number of 
vibrations: this is nevertheless not entirely exact, and Cagniard de la Tour 
has invented a special apparatus by means of which the absolute number of 
vibrations in a tone can be accurately determined. This instrument is repre- 
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