Elements of natural philosophy (Volume 2-3) . be in such relative condition that one will wholly neutralize the other, and the two produce perfect silence. This phenomenon is called the Inter-Interferencc of ,. „ •, sound. jerence ot sound. With any other values for A and A than those whichgive Af - A = 180°, Equation (26), shows that a . 2a - <—; X X Result of partialcoincidence oftwo sound waves. that is, that the sound in the resultant wave will be lessthan double that in either of the equal component waves. 60. To ascertain the precise relation between twoCoudItions tI,at i • i •ii i it
Elements of natural philosophy (Volume 2-3) . be in such relative condition that one will wholly neutralize the other, and the two produce perfect silence. This phenomenon is called the Inter-Interferencc of ,. „ •, sound. jerence ot sound. With any other values for A and A than those whichgive Af - A = 180°, Equation (26), shows that a . 2a - <—; X X Result of partialcoincidence oftwo sound waves. that is, that the sound in the resultant wave will be lessthan double that in either of the equal component waves. 60. To ascertain the precise relation between twoCoudItions tI,at i • i •ii i it W*N cailse two equal waves, which will cause one to destroy the other, equai waves to neutralize eachother. make, in Equation (20), A = A! ± 180° = A±* and we have a r —x 1 & = ~, sin (2* —^— + A ± *] but 7T = 2*. Transformations; C8 NATURAL PHILOSOPHY. and this substituted above, the equation becomes Resultantdisplacement; <T= — . sin fe*. x L V. t-x± \ x + A] Conditions inwords. When waves Fiff. which becomes identical with Equation (21) by writing x, for a? ± i X. That is to say, one wave will destroy another of equal length and intensity, provided the first he in advance or in rear of the second, ly half the length of the wave. And since the retardation of a whole length of a wave, two whole lengths, three whole lengths, &c, produces no alteration in an undulation, it is obvious that a retardation of 3 X 5 X 7 X ~2~~2~ 2 , &c, will produce the same effect as a retardation of -—: and thus two waves will destroy each other if the maxima of vi-bration be the same, the waves of the same length,and transmitted in the same direction ; provided, onefollow the other by one half, three halves, five halves, &c,of a wave length. If the waves do not proceed in thenterfere only at same direction, they will interfere only at the point ofpomt o union, ^j^ ^q above conditions being fulfilled. Same considerationsapplicable tothree or moreequal wav
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