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Unformatted text preview: FNT #4 More interference October 17, 2005 Question 1: KDVS radio station Suppose that KDVS, the campus radio station, transmitted from two an tennas placed Î»/ 4 apart in the WestEast direction. Suppose also that the constant phase of antenna A is Ï€/ 2 (90 â—¦ ) ahead of antenna B. B N S E W A Î»/4 a) For each of the four major compass points, is the interference constructive, destructive or partial? The phase difference in each case is âˆ†Î¦ = 2 Ï€ Î» ( x A x B ) + Ï† A Ï† B = 2 Ï€ Î» ( x A x B ) + Ï€ 2 as Ï† A is ahead of (i.e. greater than) Ï† 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 âˆ†Î¦ = 2 Ï€ Î» (0) + Ï€ 2 = Ï€ 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 + Î»/ 4. This leads to a total phase difference of âˆ†Î¦ = 2 Ï€ Î» ( x A x B ) + Ï€ 2 = 2 Ï€ Î» parenleftbigg a8 a8 x B + Î» 4 a8 a8 x B parenrightbigg + Ï€ 2 = 2 Ï€ a19 Î» a19 Î» 4 + Ï€ 2 = Ï€ 2 + Ï€ 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 Î»/ 4, leading to an interference of âˆ†Î¦ = 2 Ï€ Î» ( x A x B ) + Ï€ 2 = 2 Ï€ Î» parenleftbigg a8 a8 x B Î» 4 a8 a8 x B parenrightbigg + Ï€ 2 = + 2 Ï€ a19 Î» a19 Î» 4 + Ï€ 2 = + Ï€ 2 + Ï€ 2 = Ï€ which leads to destructive interference....
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This note was uploaded on 10/22/2010 for the course PHY PHY 7C taught by Professor Staff during the Spring '09 term at UC Davis.
 Spring '09
 Staff
 Physics

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