The Ray Equations. In two dimensions, we consider a poin
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The Ray Equations. In two dimensions, we consider a point sound source located at (x, y) = (x0, y0) in a fluid medium wh
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The Ray Equations. In two dimensions, we consider a point sound source located at (x, y) = (x0, y0) in a fluid medium where the sound speed c(x, y) can vary with location (see Figure 3.P.5 and Project 3 in Chapter 3 for a discussion of ray theory). The initial value problem that describes the path of a ray launched from the point (x0, y0) with a launch angle ?, measured from the horizontal, is d ds (1 c dx ds ) = ?cx c2 , x(0) = x0, x? (0) = cos ? (i) d ds (1 c dy ds ) = ? cy c2 , y(0) = y0, y? (0) = sin ?, where cx = ?c??x and cy = ?c??y. The independent variable s in Eq. (i) is the arc length of the ray measured from the source. Derive the system (i) from Fermat
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