Elements of natural philosophy (Volume 2-3) . ), upon the direction in which the sound is transmitted. A disturbed particle in a perfectly homo- ELEMENTS OF ACOUSTICS. 45 geneous medium becomes the centre of a series of con-centric spherical waves which proceed outwards withequal velocities in all directions. But if the elastic force Medmmnot x t § homogeneous; and density of the medium vary in different directions from the place of disturbance, Equation (12), shows that the shape of the wave front will no longer be spherical. It will be elongated or drawn out in the direction along wave front
Elements of natural philosophy (Volume 2-3) . ), upon the direction in which the sound is transmitted. A disturbed particle in a perfectly homo- ELEMENTS OF ACOUSTICS. 45 geneous medium becomes the centre of a series of con-centric spherical waves which proceed outwards withequal velocities in all directions. But if the elastic force Medmmnot x t § homogeneous; and density of the medium vary in different directions from the place of disturbance, Equation (12), shows that the shape of the wave front will no longer be spherical. It will be elongated or drawn out in the direction along wave front not which the elastic force is greatest and density least, and conversely. Like effects will arise when the elasticity and density both increase or decrease, but unequally. § 42. Thus, conceive a solidwhose density, estimated in thedirection A C, is represented byDn and in the direction A B byDt + c ; and suppose the density tovary gradually from one of thesedirections to the other, and the lawof this variation to be expressed by Fig. Illustration; D = j) (i + o . cos 4>), /I K\ Intermediate density; in which D denotes the density in any intermediatedirection as A D, and 0 the angle which that directionmakes with that of greatest density or with A B. Also,let the elastic force in the direction A 0 be E., and thatin the direction A i?, be measured by E. 1-c Elastic force indirection ofgreatest density; and suppose the elastic force, denoted by jE7, in the in-termediate direction A D, to be given by the relation E = E. 1 — c. cos (16). Same in intermediate direction. Dividing Eq. (16), by Eq. (15), we find 10 NATURAL PHILOSOPHY. Ratio ofintermediatedensity andelastic force; E JJ E. JJ 1 — c2 .cos2 <p and substituting this in Equation (12), and replacing Vby its measure r, the space passed over in a unit of timeby the front of the wave, we have Radius vector ofwave front; r =
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