ON INTERFERENCE. 
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independently of the other, as explained in Chap. VllI, pp. 82 & 83; crest being added to crest, and trough to trough, to produce a wave (3) of the same length as each of the coincident waves, but of twice the amplitude of either.
Now, let us suppose, that these two series of waves come together in such a way, that the crests of one exactly coincide with the troughs of the other : in other words, let them be in opposite phase as represented in fig. 68 (4) (5). In this case, by the use of the 







(6)
Fig. 68.
same kind of reasoning as employed in Chap. VIII, we find that, as the drops of water are solicited in opposite directions, by equal forces, at the same time, the result is no wave at all, fig. 68 (6). We have supposed here, that the waves in both series have the same amplitude. If they have different amplitudes, it is evident from the above, that, 1st, when the two series are in the same phase, the amplitude of the resultant wave is equal to the sum of the amplitudes of the constituents; 2nd, when the two series are in opposite phases, the amplitude of the resultant wave is equal to the difference of the amplitudes of the constituents. Further, it is evident, that if they are neither in the same nor opposite phases, the amplitude of the resultant wave will be intermediate between these two limits.
Now we may take the curves (1) (2) (4) (5) of figs. 67 and 68, as the associated waves of two simple sounds, and therefore at once deduce the following results. 1st, Two sound waves of the same length and amplitude, and in the same phase, produce a resultant wave of the same length, but twice the amplitude of either wave. 2nd, Two sound waves of the same length and amplitude, but in opposite phase, destroy one another's effects, and no wave is produced. 3rd, Two sound waves of the same length but different amplitudes, will produce a wave of the same length as either wave, but having an amplitude equal to the sum or difference of their amplitudes, 
