Q.A TV tower has height 'h'. Derive an expression for the maximum distance up to which the signal can be received from the antenna. What is the area and population covered by the signal?

Using the line-of-sight antenna range formula $d=\sqrt{2Rh}$ and solving for h with d=64 km, R=6400 km gives h=0.32 km.

Working

The line-of-sight range of a transmitting antenna of height $h$, given the Earth's radius $R$, is

$d = \sqrt{2Rh} \ \Rightarrow\ h = \dfrac{d^2}{2R}$

Given $d=64$ km, $R=6400$ km: …

Satellite links use microwaves because they travel in straight lines, are not reflected by the ionosphere, and can be tightly beamed with practical antenna sizes.

Of the electromagnetic spectrum, microwaves (wavelength range roughly mm to a few cm, frequency ~GHz) are used for satellite communication: they penetrate the ionosphere (unlike lower-frequency radio waves, which get reflected), travel by line-of-sight, and can be focused into narrow beams using dish antennas of a convenient size, all …

A geostationary communication satellite is about 36,000 km above the Earth → option (A).

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UHF (very high frequency) is transmitted as space (line-of-sight) waves.

Ground waves attenuate rapidly at high frequency, and sky waves fail above ~30 MHz because the ionosphere no longer reflects them (the waves penetrate it). UHF frequencies (300 MHz–3 GHz) therefore propagate as space waves — line …

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Space-wave propagation is used for signals in the VHF band and above, where the wave travels essentially in a straight line (line-of-sight) between transmitting and receiving antennas, since such high frequencies pass straight through the ionosphere instead of being reflected. Two everyday examples of communication systems that rely on the space-wave mode are:

1. Television broadcasting — TV signals (VHF/UHF band) cannot be reflected by the ionosphere, so they must be received via direct line-of-sight (hence tall TV transmission towers and receiving antennas). …

The 30 MHz-400 GHz band covers VHF/UHF/SHF, which travel by line-of-sight, i.e. space wave propagation.

Working

Radio wave propagation is classified by frequency:

• Ground wave propagation: up to about 2 MHz (follows the earth's curvature).
• Sky wave propagation: about 2-30 MHz (reflected back by the ionosphere). …

GPS is a satellite navigation system giving a receiver's precise location and time anywhere on Earth.

The Global Positioning System (GPS) consists of a network (constellation) of navigation satellites orbiting the Earth, each continuously transmitting signals carrying its own precise position and the exact time.

A GPS receiver on the ground (or in a vehicle, ship, aircraft, or mobile phone) picks up signals from several of these satellites simultaneously. By measuring the time delay of the signals received from at least four satellites and using the technique of trilateration, the receiver calculates its own precise three-dimensional position (latitude, longitude, and …

Range d = √(2Rh) = √(2 × 6.4×10⁶ × 245) ≈ 5.6×10⁴ m = 56 km.

For a transmitting antenna of height h, the maximum line-of-sight coverage distance on the Earth (radius R = 6.4 × 10⁶ m) is

$d = \sqrt{2Rh}.$

Substituting h = 245 m:

…

Satellites relay signals via line-of-sight space-wave propagation, directly between the ground station and the satellite.

Satellite communication uses very high frequency microwave signals sent directly (line-of-sight) between the ground station's antenna and the satellite — this direct, straight-line propagation through space is called space-wave propagation. G …