# 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?

Jan 26, 2016

I found: $t = 0.27 s$

#### Explanation:

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

Jun 20, 2018

$270 \sec . \left(= 4 \min . 30 \sec .\right)$

#### 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 $300 , 000 \frac{k m}{s}$
I take the distance you are given, to be $8.2 \cdot {10}^{7} k m$ (since $8.2 \cdot 107 k m$ 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 $4 \frac{1}{2}$ min for the radio wave to reach Mars from the earth.

Actual calculation:
$\frac{82 , 000 , 000 k m}{300 , 000 \frac{k m}{s}}$=$\frac{820}{3}$ s =$273.3$ s

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