The GPS (Global Positioning System) satellites are approximately 5.18 m across and transmit two low-power signals, one of which is at 1575.42 MHz (in the UHF band). In a series of laboratory tests on the satellite, you put two 1575.42 MHz UHF transmitters at opposite ends of the satellite. These broadcast in phase uniformly in all directions. You measure the intensity at points on a circle that is several hundred meters in radius and centered on the satellite. You measure angles on this circle relative to a point that lies along the centerline of the satellite (that is, the perpendicular bisector of a line that extends from one transmitter to the other). At this point on the circle, the measured intensity is 2.00 W/m2 . (a) At how many other angles in the range 0° < θ < 90° is the intensity also 2.00 W/m2 ? (b) Find the four smallest angles in the range 0° < θ < 90° for which the intensity is 2.00 W/m2 . (c) What is the intensity at a point on the circle at an angle of 4.65° from the centerline?
The GPS (Global Positioning System) satellites are approximately 5.18 m across and transmit two low-power signals, one of which is at 1575.42 MHz (in the UHF band). In a series of laboratory tests on the satellite, you put two 1575.42 MHz UHF transmitters at opposite ends of the satellite. These broadcast in phase uniformly in all directions. You measure the intensity at points on a circle that is several hundred meters in radius and centered on the satellite. You measure angles on this circle relative to a point that lies along the centerline of the satellite (that is, the perpendicular bisector of a line that extends from one transmitter to the other). At this point on the circle, the measured intensity is 2.00 W/m2 . (a) At how many other angles in the range 0° < θ < 90° is the intensity also 2.00 W/m2 ? (b) Find the four smallest angles in the range 0° < θ < 90° for which the intensity is 2.00 W/m2 . (c) What is the intensity at a point on the circle at an angle of 4.65° from the centerline?
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