Space wave propagation.
Range of frequencies for space wave propagation is used to transmit
VHF band   30MHz to 300 MHz
UHF band   300MHz to 3 GHz
Microwaves 100 GHz
e.g. TV signals 80 to 200 MHz and RADAR beans (microwaves).

In amplitude modulated signal, out of \(\left( { \omega }_{ c }-{ \omega }_{ m } \right) \), \({ \omega }_{ c }\) and \(\left( { \omega }_{ c }+{ \omega }_{ m } \right) \) only \(\left( { \omega }_{ c }+{ \omega }_{ m } \right) \)and \(\left( { \omega }_{ c }-{ \omega }_{ m } \right) \) contain informations. Hence cost can be reduced by transmitting \(\left( { \omega }_{ c }+{ \omega }_{ m } \right) \), \(\left( { \omega }_{ c }-{ \omega }_{ m } \right) \) or both \(\left( { \omega }_{ c }+{ \omega }_{ m } \right) \) and \(\left( { \omega }_{ c }-{ \omega }_{ m } \right) \).

For F₁ layer : 5 x 10⁶ = 9 (N_max)^1/2 or \({ N }_{ max }=\left( \frac { 5 }{ 9 } \times { 10 }^{ 6 } \right) ^{ 2 }=3.086\times { 10 }^{ 11 }{ m }^{ -3 }\)
For F₂ layer : 8 x 10⁶ = 9(N_max)^1/2  or  \({ N }_{ max }=\left( \frac { 8 }{ 9 } \times { 10 }^{ 6 } \right) ^{ 2 }=7.9\times { 10 }^{ 11 }{ m }^{ -3 }\)

Here, h₁ = 20 m, h₂ = 25 m
(i) \(d=\sqrt { 2{ h }_{ 1 }R } =\sqrt { 2\times 20\times \left( 6.4\times { 10 }^{ 6 } \right) } =16\times { 10 }^{ 3 }m=16km\)
Area covered, \(A=\pi { d }^{ 2 }=\frac { 22 }{ 7 } \times { \left( 16 \right) }^{ 2 }\simeq 804.6{ km }^{ 2 }\)
(ii) Range, \({ d }_{ 1 }=\sqrt { 2{ h }_{ 1 }R } +\sqrt { 2{ h }_{ 2 }R } =\sqrt { 2\times 20\times \left( 6.4\times { 10 }^{ 6 } \right) } +\sqrt { 2\times 25\times 6.4\times { 10 }^{ 6 } } \)
\(=16km+17.9km=33.9km\)
Area covered, \({ A }_{ 1 }=\pi { d }_{ 1 }^{ 2 }=\frac { 22 }{ 7 } \times { \left( 33.9 \right) }^{ 2 }=3611.8{ km }^{ 2 }\)
% increase in area = \(\frac { { A }_{ 1 }-A }{ A } \times 100=\left( \frac { 3611.8-804.6 }{ 804.6 } \right) \times 100=\) 348.9%