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142 |
DETURMINATION OF JOINT WAVE. |
[vi. §72 |
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as Oft is greater than Ob, as in (3), or less than Ob, as in (4). Thus, each tributary set of forces produces its full effect in its own direction, or, in other words, the displacement due to one set is superposed on that due to the other.
In order to determine the form of the resultant wave, we have only to apply this principle to successive particles. We thus obtain an assemblage of points constituting the wave required.
The problem of the motion of an air-particle engaged in transmitting simultaneously two partial-tones of a clang is, therefore, to be solved as follows. Let each simple vibration be represented by its associated wave. Ascertain by the process just described to what joint fonn the superposition of these two waves leads. The result will be the associated wave-form corresponding to the mode of particle-vibration to which the compound sound is due.
72. Before, however, we can lay down the two tributary waves, an important point remains to be settled. We will, for a moment, suppose that the two simple tones on which we are engaged are sustained by two tuning-forks situated as in the annexed figure, and that we are examining the transmission of their resulting clang along the dotted line with respect to which they are symmetrically situated. |
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