Elements of natural philosophy (Volume 2-3) . oduce 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 waves; § 61. The same process of combination may be
Elements of natural philosophy (Volume 2-3) . oduce 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 waves; § 61. The same process of combination may be ap-plied to three, four, &c, waves of equal lengths. Thuslet there be the Equations jt d - (o -, —x A,la = — sin 2 * l A x L X ^ J Equations to beused; * d=al Bin [2* I±^ + A] ELEMENTS OF ACOUSTICS. 69 d=*l sin \**:Y±?+Ai\ X L A J adding these, developing thesine of the sum of the twoarcs within the brackets, col-lecting the common factorsand denoting the resultantdisplacement by d, we have Fisr. 28. Operationsperformed;. ?n Illustration; X A x X Resultant y~ 1 displacement; or 7 W a = —. sm X 2*. - V .1 — X X in which + ^]; The same; a cos A = a cos A + a cos A + a cos A = Xa sin A = a sin J. + a sin J. +. a sin A = 3 « = r y/P+T^ tan J. = -j= • Notation. § 62. Although it is possible for two waves of sound,whose lengths are the same, to neutralize each other, it isnot so when thewaves have un-equal lengths;for, Eq. (22) Jwas deducedby making Vand X the same in the two component waves, the sumof d! and d being in that case reducible. If these con-ditions were not fulfilled, this sum would not be reducible,and there would be the two arcs
Size: 1746px × 1431px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, booksubjectmechanics, booksubjectopticsandphoto
