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# How long would it take a radio wave of frequency $6 \times {10^3}\sec$ to travel from Mars to the Earth, a distance of $8 \times {10^7}km$?

Last updated date: 29th Feb 2024
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Hint: A radio wave is an electromagnetic wave. We know that the speed of all electromagnetic waves in a vacuum is the same, irrespective of their frequency. Again, the speed of an electromagnetic wave in a vacuum is the same as that of light, i.e. $3 \times {10^8}\dfrac{m}{s}$
The distance between Earth and Mars is given. Therefore we can find the time taken to cover this distance with a speed of$3 \times {10^8}\dfrac{m}{s}$.

Formula used:
$time = \dfrac{{dis\tan ce}}{{velocity}}$
Distance = $8 \times {10^7}km$
Velocity = $3 \times {10^8}\dfrac{m}{s}$

Complete step-by-step solution:
Given that, a radio wave travels from Mars to Earth.
The radio wave is an electromagnetic wave. We know that the speed of all electromagnetic waves in a vacuum is the same, irrespective of their frequency.
The speed of an electromagnetic wave in a vacuum is the same as that of light, i.e. $3 \times {10^8}\dfrac{m}{s}$
The distance of Mars from Earth is given by$8 \times {10^7}km$, i.e. $8 \times {10^{10}}m$. $(1km{\text{ }} = {\text{ }}1000{\text{ }}m)$
Therefore, the total time taken to travel is given by:
$time = \dfrac{{dis\tan ce}}{{velocity}}$
$\Rightarrow t = \dfrac{{8 \times {{10}^{10}}}}{{3 \times {{10}^8}}}$
$\Rightarrow t = \dfrac{{800}}{3}$
$\Rightarrow t = 266.67\sec$
$\Rightarrow t = \dfrac{{266.67}}{{60}} = 4.44\min$
Hence, it will take the radio wave approximately $266.67{\text{ }}seconds$ or $4.44{\text{ }}minutes$ to travel from Mars to Earth.

Note: From the given question, the distance between Earth and Mars is given in kilometers. Change the unit to meters and proceed. We know that one kilometer is equal to ${10^3}$meter and One minute is equal to $60$ seconds.