how long it would take a radio wave of frequency 6*10^3
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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=3×108m/sc = 3\times 10^8 \, \, m/sc=3×108m/s
Also, the distance between Mars and Earth is given:
d=8×107km=8×1010md = 8 \times 10^7 \, \, km = 8\times 10^{10} \, \, md=8×107km=8×1010m
So, we can find the time taken for travel:
Velocity=DistanceTime⟹c=dt⟹t=dc⟹t=8×1010m3×108m/s⟹t=8003s⟹t=8003×60min⟹t=409min⟹t≈4.44min⟹t≈4min26.67sec\begin{lgathered}\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}\end{lgathered}Velocity=TimeDistance⟹c=td⟹t=cd⟹t=3×108m/s8×1010m⟹t=3800s⟹t=3×60800min⟹t=940min⟹t≈4.44min⟹t≈4min26.67sec
Thus, The Radio Wave will take approximately 4.44 minutes 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=3×108m/sc = 3\times 10^8 \, \, m/sc=3×108m/s
Also, the distance between Mars and Earth is given:
d=8×107km=8×1010md = 8 \times 10^7 \, \, km = 8\times 10^{10} \, \, md=8×107km=8×1010m
So, we can find the time taken for travel:
Velocity=DistanceTime⟹c=dt⟹t=dc⟹t=8×1010m3×108m/s⟹t=8003s⟹t=8003×60min⟹t=409min⟹t≈4.44min⟹t≈4min26.67sec\begin{lgathered}\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}\end{lgathered}Velocity=TimeDistance⟹c=td⟹t=cd⟹t=3×108m/s8×1010m⟹t=3800s⟹t=3×60800min⟹t=940min⟹t≈4.44min⟹t≈4min26.67sec
Thus, The Radio Wave will take approximately 4.44 minutes to travel from Mars to Earth
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