ch17-p107 - x axis from the similar one along the – x...

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107. (a) The problem is asking at how many angles will there be “loud” resultant waves, and at how many will there be “quiet” ones? We consider the resultant wave (at large distance from the origin) along the + x axis; we note that the path-length difference (for the waves traveling from their respective sources) divided by wavelength gives the (dimensionless) value n = 3.2, implying a sort of intermediate condition between constructive interference (which would follow if, say, n = 3) and destructive interference (such as the n = 3.5 situation found in the solution to the previous problem) between the waves. To distinguish this resultant along the +
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Unformatted text preview: x axis from the similar one along the – x axis, we label one with n = +3.2 and the other n = –3.2. This labeling facilitates the complete enumeration of the loud directions in the upper-half plane: n = –3, –2, –1, 0, +1, + 2, +3. Counting also the “other” –3, –2, –1, 0, +1, +2, +3 values for the lower-half plane, then we conclude there are a total of 7 + 7 = 14 “loud” directions. (b) The labeling also helps us enumerate the quiet directions. In the upper-half plane we find: n = – 2.5, –1.5, –0.5, +0.5, +1.5, +2.5. This is duplicated in the lower half plane, so the total number of quiet directions is 6 + 6 = 12....
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