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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? - CBSE (Science) Class 12 - Physics

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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.

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:

d = 50 m

Fresnel’s distance is given by the relation,

`Z_p = a^2/lambda`

Where,

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.

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Solution 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? Concept: Diffraction - The Validity of Ray Optics.
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