Question

A spaceship traveling to Alpha Centauri at 0.75c sends a message home to Earth saying they are at the halfway point.

Answer 1

Answer:

(a) 24.87 GHz (b) 3.55 GHz

Explanation:

We have given the speed of the spaceship =0.75 c, here c is the speed of the light

(a) In the first case the ship is moving towards the alpha century

So the frequency is given by  $f'=f\times \sqrt{\frac{c+0.75c}{c-0.75c}}=9.4\times \sqrt{\frac{c+0.75c}{c-0.75c}}=24.87GHz$

(b) In this case the ship is moving away from the alpha century

So frequency is given by $f'=f\times \sqrt{\frac{c-0.75c}{c+0.75c}}=9.4\times \sqrt{\frac{c-0.75c}{c+0.75c}}=3.55GHz$