HANDBOOK OF ACOUSTICS - online book

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

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146                    HAND-BOOK OF ACOUSTICS.
In order to obtain a clearer insight into this matter, let us suppose the forks in the above case to commence vibrating, as before, in exactly the same phase, and let us consider the waves produced during the first half second. As their vibration numbers are assumed to be 16 and 15, the sharper fork will have originated exactly 8, and the flatter fork exactlywaves during this period. Let the 8 equal associated waves of fig. 76 B, represent the former, as if they alone were present: and let theassociated waves of fig. 76 A, represent the latter, on the same supposition. The two series are placed one above the other, instead of being superposed, for the sake of distinctness. The forks are supposed to be at the right hand side of the figure, the waves travelling towards the left; thus the first pair of waves originated, are now on the extreme left, the next pair immediately behind these, and so on. In accordance with the supposition, the two series of waves (which, it may be noted, are not represented as of equal amplitude) commence in exactly the same phase, but in consequence of their difference in length, this exact accordance becomes less and less in succeeding waves, till at length, those on the extreme right are in exactly opposite phase. Now when the two forks are simultaneously sounding, their sound-waves combine or interfere, to produce a resultant wave, the associated wave form of which we can obtain, by compounding the two associated wave forms, A & B, in the manner before described. The thick curved line of fig. 76 C has been thus obtained; and we see from it, that the two original sound-waves coalesce, to produce a resultant sound-wave, which at first has an amplitude equal to the sum of the amplitudes of its constituent waves, but that the amplitude gradually diminishes, till in half a second, it is only equal to the difference of the amplitudes of its constituents. It is easy to see from the figure, that during the next half second, the amplitude of the resultant wave will gradually increase, till at the beginning of the next second, it will again have reached its maximum. These alternations in the amplitude of the resultant waves, produce of course in the resultant sound, corre­sponding alternations of intensity, which, as already mentioned, are termed Beats, and which may be represented in the ordinary musical way by crescendo and diminuendo marks—
It is evident from fig. 76, that half a beat is formed by the interference of the waves there represented, that is, in half a second. Therefore when two sounds, the vibration numbers of which are 15