HANDBOOK OF ACOUSTICS - online book

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

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144                    HAND-BOOK OF ACOUSTICS.
organ, by combining pipes of the same kind, under the conditions just referred to.
"We pass on to consider the case of the interference of two simple tones, which differ slightly in pitch. Let two tuning-forks, stand­ing close together, side by side, be supposed to commence vibrating together in exactly the same phase ; and for the sake of simplicity, we will suppose their vibration numbers to be very small, viz., 15 and 16 respectively. Now, although these two forks may start in exactly the same phase, that is, the prongs of each may begin to move inward or outward together, this coincidence can evidently not be maintained, since their vibration rates are different. The flatter fork will gradually lag behind the other, till, in half a second, it will be just half a vibration behind, having performed only 7^ vibrations while the other fork has performed 8. At the end of half a second, therefore, the two forks will be in complete opposition ; the prongs of the one fork moving one way, while those of the other fork are moving in the opposite. After the lapse of another half second, the flatter of the two forks will be exactly one com­plete vibration behind the other, and consequently the forks will be in exact accordance again, as they were at first. These changes will evidently recur regularly every second. Thus, assuming as we have done, that the forks are in exactly the same phase at the commencement, we find that, at the beginning of each successive second, the sound-waves from the two forks coincide, condensation with condensation, or rarefaction with rarefaction, to produce a sound-wave of greater amplitude than either; but at the half seconds, the two series of sound waves will interfere, the conden­sation of one with the rarefaction of the other, to produce a sound­wave of less amplitude, or even, if the amplitudes of the two waves are equal, to produce momentarily, no sound wave at all. These changes in the amplitude of the resultant wave will evidently be gradual, so that the effect on the ear will be as follows: at the commencement, a sound of considerable intensity will be heard; during the first half second, its intensity will diminish, till at the exact half second, it is at a minimum, or may even be nil; during the next half second the intensity will increase, till at the beginning of the next second the sound has the same intensity as at first. Precisely the same changes will occur during each successive second; so that a series of crescendos and diminuendos, or swells, will be heard, one crescendo and one diminuendo being produced in the present supposed case, every second.