Subjective Type

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 is 40km.
Height of the line joining the hills is $$d=50m$$.
Thus, the radial spread of the radio waves should not exceed 50 m.
Since the hill is located halfway between the towers, Fresnel’s distance can be obtained.
$$Z_P=20km$$
Aperture is $$a=d=50m$$
Fresnel’s distance is given by the relation,
$$Z_P=a^2/\lambda=2\times 10^4$$
$$\lambda=a^2/Z_P=12.5cm$$

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