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How long would it take a radio-wave of frequency $6 \times {10^3}{\sec ^{ - 1}}$ to travel from Mars to the Earth, a distance of $8 \times {10^7}$ km?

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Last updated date: 19th Jun 2024
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Answer
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Hint: Radio wave is an electromagnetic wave. We know that the speed of all electromagnetic waves in vacuum is the same, irrespective of their frequency. Again, speed of an electromagnetic wave in vacuum is same with that of light, i.e. $3 \times {10^8}$ 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 $3 \times {10^8}$ m/s.

Formula used: ${\text{time}} = \dfrac{{{\text{distance}}}}{{{\text{velocity}}}}{\text{ }}$

Complete step by step answer:
Given that, a radio wave travels from Mars to Earth.
Radio wave is an electromagnetic wave. We know that the speed of all electromagnetic waves in vacuum is the same, irrespective of their frequency.
The speed of an electromagnetic wave in vacuum is same with that of light, i.e. $3 \times {10^8}$ m/s
The distance of Mars from Earth is given by $8 \times {10^7}$ km, i.e. $8 \times {10^{10}}$ metres.
Therefore, the total time taken to travel is given by:
${\text{time}} = \dfrac{{{\text{distance}}}}{{{\text{velocity}}}}{\text{ }}$
$ = \dfrac{{8 \times {{10}^{10}}}}{{3 \times {{10}^8}}}$
$ = \dfrac{{800}}{3}$
$ = 266.67$seconds
$ = \dfrac{{266.67}}{{60}} = 4.44$ minutes

Hence, it will take the radio wave approximately 266.67 seconds or 4.44 minutes to travel from Mars to Earth.

Note: Radio wave is an electromagnetic wave. We know that the speed of all electromagnetic waves in vacuum is the same, irrespective of their frequency. The speed of an electromagnetic wave in vacuum is same with that of light, i.e. $3 \times {10^8}$ m/s
Note that the distance between Earth and Mars is given in kilometers. Change the unit to meters and proceed.