Two towers on top of two hills are 40 km apart.

Question:
Two towers on top of two hills are 40 km apart. The line joining them passes 50 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?

Solution:

Distance between the towers = 40 km

Height of the line joining the hills, d = 50 m

The radial spread of the radio waves must not exceed 50 m

Aperture a = d = 50 m

The hill is located halfway between the towers. Therefore, Fresnel’s distance is Zp = 20 km

Fresnel’s distance can be given by the equation, Zp = a2/λ

λ = a2/Zp

= (50)2/(20 x 103)

= 250/20 = 12.5 x 10-3 m = 12.5 cm

Two towers on top of two hills are 40 km apart.

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