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Unformatted text preview: FNT #4 More interference August 15, 2005 Question 1: KDVS radio station Suppose that KDVS, the campus radio station, transmitted from two an tennas placed / 4 apart in the WestEast direction. Suppose also that the constant phase of antenna A is / 2 (90 ) ahead of antenna B. B N S E W A /4 a) For each of the four major compass points, is the interference constructive, destructive or partial? The phase difference in each case is = 2 ( x A x B ) + A B = 2 ( x A x B ) + 2 as A is ahead of (i.e. greater than) B . (The minus sign is because the wave is travelling out, so that as t increases the positive distance from both station A and station B increases.) North and south The path difference for a point on the northsouth axis is zero, as x A = x B . 1 B B x A x N S E W A The total phase difference is then = 2 (0) + 2 = 2 which is partial interference. East A B x B x N S E W A For a point in the East we have x A = x B + / 4. This leads to a total phase difference of = 2 ( x A x B ) + 2 = 2 parenleftbigg a8 a8 x B + 4 a8 a8 x B parenrightbigg + 2 = 2 a19 a19 4 + 2 = 2 + 2 = 0 which means that we have constructive interference in the East. West B B x A x N S E W A 2 For a point in the West we have x A = x B / 4, leading to an interference of = 2 ( x A x B ) + 2 = 2 parenleftbigg a8 a8 x B 4 a8 a8 x B parenrightbigg + 2 = + 2 a19 a19 4 + 2 = + 2 + 2 = which leads to destructive interference. b) Why would they choose to do this? Where should KDVS set up their radio station?...
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 Spring '09
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 Physics

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