As part of a physics lab practical exam, you are dropped off in the woods with an EM field meter and a compass. Your task is to find your way to a radio beacon (broadcasting with P=10 kW) somewhere to the north of you. You set your EM field meter to pick up the beacon frequency f=2 kHz.
(a) You are dropped off a distance R1 from the beacon where the EM meter reports the signalâ€™s intensity as . After a short walk, the meter reports the signals intensity as I2=(2.25 I1). In terms of your current position R2, what was your original distance from the beacon R1?
(b) The short walk you took in part (a), was really a bit of a hike. Specifically, you hiked a=3 km due north and then b=5 km due west. Also, your first signal intensity measurement was I1= 5.53 uW/m^2. Assuming that the beacon broadcasts like a point source, what are R1 and R2 as measured in kilometers?
(c) At what compass bearing is the beacon relative to your position at R2? (Measure your angles from due east.)