Question

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?

Answer 1

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.

Answer 2

`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.