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?
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, Fresnel’s distance can be obtained as:
ZP = 20 km = 2 × 104 m
Aperture can be taken as:
a = d = 50 m
Fresnel’s distance is given by the relation,
`Z_p = a^2/lambda`
λ = Wavelength of radio waves
`:. lambda = a^2/Z_p`
`= (50)^2/(2xx10^4) =- 1250 xx 10^(-4) = 0.1250 m = 12.5 cm`
Therefore, the wavelength of the radio waves is 12.5 cm.