Question

The maximum frequency for reflection of sky waves from a certain layer of the ionosphere is found to be f_max = 9(N_max)^1/2, where Nmax is the maximum electron density at that layer of the ionosphere. On a certain day, it is observed that signals of frequencies higher than 5 MHz are not received by reflection from the F₁ layer of the ionosphere while signals of frequencies higher than 8 MHz are not received by reflection from the F₂ layer of the ionosphere. Estimate the maximum electron densities of the F₁ and F₂ layers on that day.

Answer 1

`d_m^2 = 2(R + h_T)^2`

`8Rh_T = 2(R + h_T)^2`  ......(∵ `dm = 2sqrt(2Rh_T))`

`4Rh_T = R^2 + h_T^2 + 2Rh_T`

`(R - h_T)^2` = 0

`R = h_T`

Since space wave frequency is used, λ << h_T, hence only tower height is taken into consideration. In three dimensions, 6 antenna towers of h_T = R would do.