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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 λ/ 4 apart in the WestEast direction. Suppose also that the constant phase of antenna A is π/ 2 (90 ◦ ) ahead of antenna B. B N S E W A λ/4 a) For each of the four major compass points, is the interference constructive, destructive or partial? The phase difference in each case is ∆Φ = 2 π λ ( x A x B ) + φ A φ B = 2 π λ ( x A x B ) + π 2 as φ A is ahead of (i.e. greater than) φ 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 ∆Φ = 2 π λ (0) + π 2 = π 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 + λ/ 4. This leads to a total phase difference of ∆Φ = 2 π λ ( x A x B ) + π 2 = 2 π λ parenleftbigg a8 a8 x B + λ 4 a8 a8 x B parenrightbigg + π 2 = 2 π a19 λ a19 λ 4 + π 2 = π 2 + π 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 λ/ 4, leading to an interference of ∆Φ = 2 π λ ( x A x B ) + π 2 = 2 π λ parenleftbigg a8 a8 x B λ 4 a8 a8 x B parenrightbigg + π 2 = + 2 π a19 λ a19 λ 4 + π 2 = + π 2 + π 2 = π 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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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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