Elements of natural philosophy (Volume 2-3) . d the intensities cannot be equal at the placesof interference, and therefore can only partially neutralizeeach others effects. This is shown by Equation (26), in which — is zero, only because #, under the conditions x there imposed, is the same denominator for a and o!\In sound, X varies, as we have seen, § 48, from a fewinches to many feet, and as the difference of intensities inthe interfering waves will be greater as X is greater, thegraver sounds would be heard, under the circumstanceswe have been considering, more audibly than the moreacute.
Elements of natural philosophy (Volume 2-3) . d the intensities cannot be equal at the placesof interference, and therefore can only partially neutralizeeach others effects. This is shown by Equation (26), in which — is zero, only because #, under the conditions x there imposed, is the same denominator for a and o!\In sound, X varies, as we have seen, § 48, from a fewinches to many feet, and as the difference of intensities inthe interfering waves will be greater as X is greater, thegraver sounds would be heard, under the circumstanceswe have been considering, more audibly than the moreacute. If the lengths X, were insensible in comparisonwith the route travelled, there would be but little in-flexion ; since, in that case, the intensities of sound in theinterfering waves would be sensibly the same, and itwould require but a slight obliquity from the directcourse of the main wave to make a difference of routeB 0 — A O, Fig. 31, equal to \\ necessary for one wavesensibly to destroy the other. ELEMENTS OF ACOUSTICS. 75 Fte. Person behind awall listening toa band of music; An auditor placed behind a wallat jP, would hear the bass notesfrom a band of music playing at aposition A on the opposite side, muchmore distinctly than the acute jP, the notes of the tuba, forinstance, might be heard distinctly,while those of the octave flute wouldbe lost to him. In passing from theposition P to 0, he would catch insuccession the higher notes in order of the ascendingscale, and finally, when he attained a position near the Position whencedirect line A 0, drawn from A tangent to the corner, he a]1 thewould hear all the instruments with equal distinctness, if equally with equal intensity and emphasis. The factsand explanations here given have an important applica-tion in the subject of optics. If we suppose the lengths of sonorous waves propagatedthrough water to be much shorter than those through theair, we have here a full and satisfactory explanati
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