Question

How long would it take a radio wave of frequency 6 X 103 hertz to travel from Mars to Earth. { distance between Mars and Earth is 8 X 107 km}.

Answer 1

We are given a Radio Wave, which has to travel from Mars to Earth.

A Radio Wave is an Electromagnetic Wave, and all Electromagnetic Waves travel with the same speed in vacuum, regardless of the frequency.

So, the frequency is unessential. We know that the speed of electromagnetic waves in vacuum is:

$c = 3\times 10^8 \, \, m/s$

Also, the distance between Mars and Earth is given:

$d = 8 \times 10^7 \, \, km = 8\times 10^{10} \, \, m$

So, we can find the time taken for travel:

$\text{Velocity} = \frac{\text{Distance}}{\text{Time}} \\ \\ \\ \implies c = \frac{d}{t} \\ \\ \\ \implies t = \frac{d}{c} \\ \\ \\ \implies t = \frac{8\times 10^{10} \, \, m}{3\times 10^8 \, \, m/s} \\ \\ \\ \implies t = \frac{800}{3} \, \, s \\ \\ \\ \implies t = \frac{800}{3 \times 60} \, \, min \\ \\ \\ \implies t = \frac{40}{9} \, \, min \\ \\ \\ \implies \boxed{t \approx 4.44 \, \, min} \\ \\ \\ \implies \boxed{t \approx 4 \, \, min \, \, 26.67 \, \, sec}$

Thus, The Radio Wave will take approximately 4.44 minutes to travel from Mars to Earth

Answer 2

Answer:

Explanation:

the frequency is unessential. We know that the speed of electromagnetic waves in vacuum is:

c = 3\times 10^8 \, \, m/s

Also, the distance between Mars and Earth is given:

d = 8 \times 10^7 \, \, km = 8\times 10^{10} \, \, m

So, we can find the time taken for travel:

\text{Velocity} = \frac{\text{Distance}}{\text{Time}} \\ \\ \\ \implies c = \frac{d}{t} \\ \\ \\ \implies t = \frac{d}{c} \\ \\ \\ \implies t = \frac{8\times 10^{10} \, \, m}{3\times 10^8 \, \, m/s} \\ \\ \\ \implies t = \frac{800}{3} \, \, s \\ \\ \\ \implies t = \frac{800}{3 \times 60} \, \, min \\ \\ \\ \implies t = \frac{40}{9} \, \, min \\ \\ \\ \implies \boxed{t \approx 4.44 \, \, min} \\ \\ \\ \implies \boxed{t \approx 4 \, \, min \, \, 26.67 \, \, sec}