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 x 10⁴ m

Aperture can be taken as: a = d = 50 m

Fresnel’s distance is given by the relation,
Z_p =a²/λ
Where, λ = Wavelength of radio waves ,

Therefore , λ =a²/Z_p 

= (50)²/ 2 x 10⁴ 

= 1250 x 10⁻⁴ = 0.1250 m = 12.5 cm

(50)’                    .

= -^—4-= 1250×10 ⁴ =0.1250 m = 12.5 cm 2×10

Therefore, the wavelength of the radio waves is 12.5 cm.