Two radio antennas separated by d = 304 m, as shown in the figure below, simulta

Question

Two radio antennas separated by d = 304 m, as shown in the figure below, simultaneously transmit identical signals of the same wavelength. A radio in a car traveling due north receives the signals. http://www.webassign.net/sercp/p24-7.gif (a) If the car is at the position of the fourth maximum, what is the wavelength of the signals? m (b) How much farther must the car travel to encounter the next minimum in reception? (Hint: Determine the path difference between the two signals at the two locations of the car.) m

Explanation / Answer

path dierence :
d sin = d sin(arctan(400/1000))
= d sin(21.8 ) = 304 sin(21.8 ) = 112.89 m ---> Answer

(a) = 4.

Therefore, = 112.89/4 = 28.22 m.---> Answer

(b)

d sin = (4 + 0.5) = 126.99.

Therefore, = arcsin(126.99/304) = 24.65 .
Therefore, y = L tan = 458.89.
y = 458.89 400 = 59 m.---> Answer

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