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140                     HAND-BOOK OF ACOUSTICS.
will be seen, that this is the case, when the right hand branch is half a wave-length longer than the left hand branch, that is, when a b is equal to one fourth of a wave-length. Thus, this instrument may be used, not only to demonstrate the phenomenon of Inter­ference, but also for roughly ascertaining the wave-length, and hence the pitch of a simple tone.
The vibrating plate (fig. 72) is a very convenient instrument with which to illustrate the phenomenon of interference. In the brief
Fig. 72.
description of this instrument given in Chap. XI, it was stated that adjacent sectors are always in opposite phase; that is, while one sector is moving upwards, the adjacent ones are moving downwards. If this be the case, it follows, that the sound waves originated above two adjacent sectors are in opposite phase, and thus interfere with one another, to diminish the resultant sound. Accordingly, if the hand be placed above any vibrating sector, the sound is not diminished, but increased. Still more is this the case if the cardboard or wooden sectors, on the right of fig. 72, be held over the segments of the plate when vibrating as shown in the figure; interference being then completely abolished, the remaining
A |           segments sound much more loudly. Thus, by sacri-
ficing a part of the vibrations, the remainder are rendered more effective.
The effect of the interference of adjacent sectors may be rendered visible, by the additional apparatus shown in fig. 73. A B is a tube which branches into two at the bottom, and is closed at A by a mem­brane, upon which a few grains of sand are scattered. Holding the ends of the branches over adjacent
Fig. 73.
segments, the membrane is unaffected, and the sand