Question

Two astronauts are 2.00 m apart in their spaceship. One speaks to the other. The conversation is transmitted to earth via electromagnetic waves. The time it takes for sound waves to travel at 354 m/s through the air between the astronauts equals the time it takes for the electromagnetic waves to travel to the earth. How far away from the earth is the spaceship?

Answer 1

Answer:

$D=1693742.7m$

Explanation:

For sound waves we have v=d/t where v is the speed of sound and d the distance between the astronauts, while for electromagnetic waves we have c=D/t where c is the speed of light and D the distance between the spaceship and Earth. We have written both times as the same because is what is imposed by the problem, so we have t=d/v=D/c, which means:

$D=\frac{dc}{v}$

And for our values:

$D=\frac{(2m)(299792458m/s)}{354m/s}=1693742.7m$