Two radio antennas separated by d = 270 m as shown in the figure below simultane

Question

Two radio antennas separated by d = 270 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 = 1 430 m from the center point between the antennas, and its radio receives the signals. Note: Do not use the small-angle approximation in this problem.

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

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

Explanation / Answer

path differenece P=dsin thetha

=dsin(arctan(400/1430))

=dsin(15.58)

=270 sin(15.58)

=72.5m

P = 2(second maximum)

72.5=2

72.5/2=

36.25m=--answer to a

b) dsinthetha=(2+0.5)

=2.5*36.25

=90.6

thetha=arcsin(90.6/270)

=19.4 degrees

so y=Ltan thetha

y=1430tan (19.4)

y=503.58

delta y=503.48-400

=103.48m--answer for part b

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