Find frequency given wavelength and distance travelled

[MrMoose]

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 into 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

Thanks in advance, MrMoose

 

[MrMoose]

Ok, I just got the right answer. The wave speed, v, is the speed of light, c:

v = c

With this knowledge, you can move on to steps 4 and 5 and get the right answer.

My next question is... why? I though EM waves only travel at the speed of light through a vacuum. Should I have assumed that this experiment was conducted in a vacuum? I don't see how I would have known that.