A TV transmitting antenna is 70 m tall. If the receiving antenna is at ground level, then the area it can cover is: (Radius of Earth = 6400 km)

Question

The percentage of the total power carried by the sidebands of the AM wave for tone modulation when the modulation index is 0.3 is:

Answer 1

Step 1: Height unit conversion.
Antenna height h = 70 m = 0.07 km.

Step 2: Line-of-sight formula.
d = √(2Rh), with Earth radius R = 6400 km.

Step 3: Numerical substitution.
d = √(2 × 6400 × 0.07) = √896 ≈ 29.93 km.

Step 4: Coverage area computation.
Circular coverage A = π d² = π × 896.

Step 5: Final value.
A ≈ 2816 km².

List-I (Modulation Schemes)	List-II (Wave Expressions)
(A) Amplitude Modulation	(I) \( x(t) = A\cos(\omega_c t + k m(t)) \)
(B) Phase Modulation	(II) \( x(t) = A\cos(\omega_c t + k \int m(t)dt) \)
(C) Frequency Modulation	(III) \( x(t) = A + m(t)\cos(\omega_c t) \)
(D) DSB-SC Modulation	(IV) \( x(t) = m(t)\cos(\omega_c t) \)

A TV transmitting antenna is 70 m tall. If the receiving antenna is at ground level, then the area it can cover is: (Radius of Earth = 6400 km)

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The Correct Option is D

Solution and Explanation

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