Two radio antennas separated by d = 272 m, as shown in the figure below, simulta

Question

Two radio antennas separated by d = 272 m, as shown in the figure below, simultaneously broadcast identical signals at the same wavelength. A car travels due north along a straight line at position

x = 1,200 m

from the center point between the antennas, and its radio receives the signals. Hint: Do not use the small-angle approximation in this problem.

(a) If the car is at the position of the third maximum after that at point O when it has traveled a distance of y = 400 m northward, what is the wavelength of the signals?

(b) How much farther must the car travel to encounter the next minimum in reception?

Explanation / Answer

a)

tan = 400/1200 = 1/3

theta = 18.44 degrees

lambda = d*sin theta/2 =(272*sin 18.44)/2 = 43.02 m

b)

sin(theta) = 5*43.02/2*272 = 0.3954

theta = 23.29 degrees

ymin = 1200*tan 23.29 = 516.55 m

additional distance = 516.55 - 400 = 116.55 m

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