How long (in seconds) does it take for a radio wave of frequency 8.94 × 106 s–1 to reach Mars when Mars is 8.2 × 107 km from Earth?

2 Answers
Gió
Jan 26, 2016

I found: #t=0.27s#

Explanation:

You radio wave should travel at the speed of light in vacuum #c=3xx10^8m/s#
so basically it would take (velocity=distance/time rearranged):
#t=d/c=(8.2xx10^10)/(3xx10^8)=273s# to reach Mars.

Roy Ø.
Jun 20, 2018

#270 sec. (=4 min. 30 sec.)#

Explanation:

Any radio wave is moving at the speed of light, regardless of the frequency, so the frequency should be superfluous information.

The speed is light is close to #300,000 (km)/s#
I take the distance you are given, to be #8.2*10^7 km# (since #8.2*107 km# doesn't make good sense - it's less than 1000 km)
i.e. #82,000,000# km.

Before we actually compute this, we can notice that this is a little more than half the distance of the earth from the sun (150 mill. km), a distance the light uses 500 sek. = 8 min 20 sec. to travel, so we should get about #4 1/2# min for the radio wave to reach Mars from the earth.

Actual calculation:
#(82,000,000 km)/(300,000 (km)/s)#=#820/3# s =#273.3# s

As the distance is given with 2 significant figures, we round this off to 270 sek = 4 min 30 sec.

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