Interference: GPS Transmission

[Fizzicist]

Homework Statement

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 which extends from one transmitter to the other). At this point on the circle, the measured intensity is 2.00 W/m^2 .

A. At how many other angles between 0 and 90 degrees is the intensity 2 W/m^2?

B. Of these angles, find the four smallest ones.

Homework Equations

A & B.

I = Iocos^2(((pi * d)/(wavelength))*sin theta)

where d is the distance between the transmitters and Io is the maximum intensity.

The Attempt at a Solution

A. I used the above equation to solve for the value at which Intensity would be 2. However, I only determined that there was 1 value between 0 and 90 based on the equation. Is there something I'm doing wrong?

 

[anathema]

B. The four smallest angles would be 0, 30, 60, and 90 degrees. Is this correct?


Your solution for part A is correct. There is only one angle between 0 and 90 degrees at which the intensity is 2 W/m^2.

For part B, the four smallest angles would be 0, 30, 60, and 90 degrees. To find these angles, you can use the inverse cosine function (cos^-1) to solve for theta in the equation I = Iocos^2(((pi * d)/(wavelength))*sin theta). Plug in the values for Io, d, and wavelength, and solve for theta. This will give you the angles at which the intensity is 2 W/m^2. Then, you can choose the four smallest angles from this list.

 

[Moetasim]

B. The four smallest angles can be found by setting the equation above equal to 2 and solving for theta. This will give you four different angles between 0 and 90 degrees.