Points A and B are 68.0 m apart along an east-west line. At each of these points
ID: 1413066 • Letter: P
Question
Points A and B are 68.0 m apart along an east-west line. At each of these points, a radio transmitter is emitting a 11.5 MHz signal horizontally. These transmitters are in phase with other and emit their beams uniformly in a horizontal plane. A receiver is taken 0.400 km north of the AB line and initially placed at point C, directly opposite the midpoint of AB. The receiver can be moved only along an east-west direction but, due to its limited sensitivity, it must always remain within a range so that the intensity of the signal it receives from the transmitter is no less than 14 of its maximum value.
Explanation / Answer
If the intensity is to be 1/4,
then I0 / 4 = I0cos² ( / 2)
= 2.09... rad
= (2 / ) d
d = 8m
The path difference is therefore 8m.
sqrt [(68m^2 + x²) + (400m)²] - sqrt [x² + (400m)²] = 8m
x = 13.6 m
distance = 68/2 + 13.6
= 47.6 m