Question

Two towers on top of two hills are $40\text{km}$ apart. The line joining them passes $50\text{m}$ above a hill halfway between the towers. What is the longest wavelength of radio waves, which can be sent between the towers without appreciable diffraction effects?

Answer 1

Given,
Distance between the two towers $=40\text{km}$
The hill is located halfway between the towers.
So, Fresnel’s distance will be half of the distance between the towers,
$Z_F=20\text{km}=2\times {10}^{4}m$
Height of the line joining of the hills,
$d=50m$
So, the radial spread of the radio waves should not exceed $50m$.
Aperture, $a=d=50m$.
Let maximum wavelength of the radio wave be $\lambda$.
Now, Fresnel’s distance $Z_F=\frac{a^2}{\lambda }$
$\lambda =\frac{a^2}{Z_F}$
$\lambda =\frac{(50{)}^2}{2\times {10}^4}=0.125\text{m}$
$\lambda =12.5\text{cm}$
Final Answer: $12.5\text{cm}$.