P18_012 - 2 x = 2 D sin = 4 sin . (a) or maximum signal, we...

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12. It is useful to study Sample Problem 18-3 before working this problem. We label the two point sources 1 and 2 and assume they are on the x axis (a distance D =2 λ apart). When we refer to the circle of large radius, we are assuming that a line drawn from source 1 to a point on the circle and a line drawn to it from source 2 are approximately parallel (and thus both at angle θ measured from the y axis). In terms of the theory developed in § 18-4, we Fnd that the phase di±erence at P (on the large circle of radius R ) for the two waves emitted from 1 and 2 is
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Unformatted text preview: 2 x = 2 D sin = 4 sin . (a) or maximum signal, we set = 2 m ( m = 0 , 1 , 2 ,... ) to obtain sin = m/ 2. Thus we get a total of 8 possible values of between 0 and 2 , given by = 0 , sin 1 (1 / 2) = 30 , sin 1 (1) = 90 and (using symmetry properties of the sine function) 150 , 180 , 210 , 270 , and 330 . (b) Since there must be a mininum in between two successive maxima, the total number of minima is also eight....
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