Question

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

(a) What is the frequency (in GHz) of the message that Earth listeners receive if it was sent at 9.4 GHz?

GHz

(b) If the ship's transmitter is omnidirectional, what is the frequency (in GHz) measured at Alpha Centauri?

GHz

Answer 1

(a) 24.87 GHz (b) 3.55 GHz

Step-by-step 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* \sqrt{(c+0.75c)/(c-0.75c)}=9.4* \sqrt{(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* \sqrt{(c-0.75c)/(c+0.75c)}=9.4* \sqrt{(c-0.75c)/(c+0.75c)}=3.55GHz`