HANDBOOK OF ACOUSTICS - online book

A complete view of Acoustical Science & its bearings on music, for musicians & music students.

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138
HAND-BOOK OF ACOUSTICS.
according as the waves are in the same or opposite phase. 4th, If the two sound waves are not exactly in the same or opposite pnase, the amplitude of the resultant wave will be intermediate between these limits.
If one sound wave have twice the amplitude of another, the intensity of the tone produced by the one will be four times that produced by the other, since intensity varies as the square of the amplitude. It follows therefore from the above, that when two simple tones of the same pitch and intensity are sounded together, the two may so combine as to produce 1st, a simple tone of the same pitch, but of four times the intensity of either of them ; 2nd, silence; or 3rd, a simple tone of the same pitch, but intermediate in intensity between these two limits ; according as their sound waves come together in the same, opposite, or intermediate phases.
The fact that two sounds may so interfere with one another as to produce silence, strange as it may seem at first, can be demonstrated experimentally, and is a special case of the general phenomenon of " Interference of waves." The only difficulty in the experimental proof, is to obtain sound waves of equal length and intensity, and in exactly opposite phase. Before explaining the way in which this difficulty can be overcome, we shall take the following supposititious case.
Let A and B (fig. 69) be two tuning-forks of the same pitch, and let us consider only the right hand prongs A and B. Now if these
Fig. 69.
prongs are in the same phase, that is, both swinging to the right and left, at exactly the same times, and if they are exactly a wave­length apart, it is evident that the two series of waves passing along A C, originated by their oscillation, will exactly coincide, condensation with condensation, and rarefaction with rarefaction, as represented by the dark and light shading. The same thing will occur, if the distance between A and B be two, three, four, or any whole number of wave-lengths. But suppose the distance from A to B were only half a wave-length, as represented in fig. 70 ; evidently, the condensations from the one fork will coincide with the rarefactions from the other, and thus the air to the right of B