Two radio antennas separatedby d = 277 m, as shown in Figure P24.7 (well, atleas

Question

Two radio antennas separatedby d = 277 m, as shown in Figure P24.7 (well, atleast except for the 300m length that is probably different foryour version), simultaneously transmit identical signals of thesame wavelength. A radio in a car traveling due north receives thesignals. (a) If the car is at the position of the fourth maximum, what is the wavelength of thesignals?(Hint: Determine the path difference between the twosignals and go from there. Note, however, the usual small - angleapproximation that sine equals tangent will NOT work here, eitherfor part a or part b.) (b) How much farther must the car travel to encounter the nextminimum in reception?

Explanation / Answer

d = 277 m, L = 1000 m, a = 400 m a) path difference = [L2 + (a + d/2)2]- [L2 + (a - d/2)2] = 4 = {[L2 + (a + d/2)2] -[L2 + (a - d/2)2]}/4 = 25.5 m b) [L2 + (a + x + d/2)2] -[L2 + (a + x - d/2)2] = 4 +/2 [L2 + (a + x + d/2)2] -[L2 + (a + x - d/2)2] = 114.9 m x = 60 m

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