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?
Answer:
Distance between the towers, (d) = 40 km
Height of the line joining the hills (d) = 50 m.
Thus, the radial spread of the radio waves should not exceed 50 km.
Since the hill is located halfway between the towers, Fresnels distance can be obtained as:
Zp = 20 Km = 2 x 104 m
Aperture can be taken as
a = d = 50 m
Fresnels distance is given by the relation,
Zp = α2/λ Where, λ = Wavelength of radio waves
Then
λ = α2/Zp = (50)2/ 2 x 104 = 1250 x 10-4 = 1250 m = 12.5 cm
Therefore, the wavelength of the radio waves is 12.5 cm.
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