Question

Two astronauts are, 6.207 m apart in their spaceship, speaking to each other. The conversation is transmitted to Earth via electromagnetic waves traveling at the speed of light. The time it takes for the sounds waves to travel at 343 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

Sol: given values are

d= 6.207m ,distance between the astronauts

Vs = 343m/s ,speed of sound waves

Vl = 3× 10^8 m/s ,speed of light

D =? , distance between earth and the spaceship

Now ,

Speed = distance/time

In case 1 when astronauts talks the time taken is given by

t = d/Vs

= 6.207/343

= 0.0180s

This is also the same time taken by sound to reach earth

again , speed = distance/time

Then distance = speed × time

= 3×10^8 × 0.0180

= 0.054×10^8

D =5.4 × 10^6 m

This is the required distance