Question

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 \[8 \times {10^7}km\]?

Answer 1

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.