# Find frequency given wavelength and distance travelled

## Homework Statement

Project Seafarer was an ambitious program to construct an enormous antenna, buried underground on a site about 4000 square miles in area. Its purpose was to transmit signals to sub-marines while they were deeply submerged. If the effective wavelength was 1.0x10^4 Earth Radii, what would be (a) the frequency and (b) the period of the radiations emitted? Ordinarily electromagnetic radiations do not penetrate very far in to conductors such as seawater.

## Homework Equations

f = 1/T where:

f: frequency
T: period

v = λf where:

v: wave speed
λ: wave length
f: frequency

Mean Earth Radii: 6.37 x 10^6 m

## The Attempt at a Solution

I'm having a lot of trouble with the wording of this problem. This is my thought process:

1. The site is 4000 square miles or ~ 63miles X 63 miles. I'm assuming the antenna is in the center of the site which would give it a radial coverage of 31.6 miles (50.855 km).

2. I think "1.0x10^4 Earth Radii" means 1.0x10^4 * Earth Radii so, λ = 6.37x10^10 m

3. Somehow use information from steps 1 and 2 to determine wave speed, but there's a few variables I don't know. For example, if I knew how long it took for the wave to travel 31.6 miles, I would be able to determine the wave speed. I'm stuck on this step.

4. Use f = v/λ to find the frequency

5. Use T = 1/f to find the period