Problem

Your intercontinental telephone call is carried by electromagnetic waves routed via a sate...

Your intercontinental telephone call is carried by electromagnetic waves routed via a satellite in geosynchronous orbit at 36,000 km altitude. Approximately how long does it take before your voice is heard at the other end?

Step-by-Step Solution

Solution 1

During an intercontinental call, the electromagnetic waves have to travel from Earth to the satellite and then from the satellite to Earth.

The distance between the geosynchronous satellite and Earth is \(d=36,000 \mathrm{~km}\) The total distance traveled by EM waves \(=2 d\)

$$ \begin{aligned} &=2(36000 \mathrm{~km}) \\ &=72 \times 10^{6} \mathrm{~m} \end{aligned} $$

$$ \begin{aligned} &\therefore \text { Velocity of EM waves } c=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \\ &\because \text { Velocity }=\frac{\text { distance }}{\text { time }} \end{aligned} $$

Thus, time taken for EM waves to travel \(t=\frac{\text { distance traveled by EM waves }}{\text { velocity of EM waves }}\)

$$ \begin{aligned} &=\frac{2 d}{c} \\ &=\frac{72 \times 10^{6} \mathrm{~m}}{3 \times 10^{8} \mathrm{~m} / \mathrm{s}} \\ &=24 \times 10^{-2} \mathrm{~s} \\ &=240 \mathrm{~ms} \end{aligned} $$

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