Question

How long (in seconds) does it take for a radio wave of frequency $8.94\times {{10}^{6}}{{s}^{-1}}$ to reach Mars when Mars is $8.2\times {{10}^{7}}km$ from Earth?

Answer 1

Hint: As a first step, recall that all electromagnetic waves move with the velocity of light which is a universal constant. As radio waves are one among the electromagnetic waves, we have the velocity. Now we could easily calculate the time taken from the distance given in the question and this velocity.
Formula used:
Expression for time in terms of distance and velocity,
$t=\dfrac{x}{v}$

Complete answer:
In the question we are given certain information regarding a radio wave. The frequency of the radio wave is given as,
$f=8.94\times {{10}^{6}}{{s}^{-1}}$
Then, we are given the distance of Mars from Earth as,
$x=8.2\times {{10}^{7}}km$
You may recall that the radio waves are actually electromagnetic waves, so we have the velocity of the radio wave from that fact. We know that the electromagnetic waves travel with the velocity of light that is,
$v=3\times {{10}^{8}}m/s=3\times {{10}^{5}}km/s$
Now you may recall that the velocity is defined as the distance covered per unit time. That is,
$v=\dfrac{x}{t}$
Rearranging, we get time as,
$t=\dfrac{x}{v}$
Substituting the values,
$t=\dfrac{8.2\times {{10}^{7}}km}{3\times {{10}^{5}}km/s}$
$\therefore t=2.73s$
Therefore, we found that the radio wave takes 2.73seconds to reach mars when the distance between Mars and Earth is the same value as that given in the question.

Note:
The time taken by the radio wave or any other wave is independent of frequency. So the value of frequency serves no purpose in solving the given question. Always one should avoid getting deviated because of such superfluous information. Also, while calculating, make sure that all quantities are substituted in the same units.