Final answer:
The frequency received on Earth for a space probe moving towards Earth at 0.250c and sending signals at 1.00 GHz appears to be 1.333 GHz after considering the Doppler effect. However, this is not one of the given options. If the space probe were moving away, the frequency would be 0.750 GHz.
Step-by-step explanation:
The frequency received on Earth when a space probe speeding towards the nearest star at 0.250c sends radio information at a broadcast frequency of 1.00 GHz can be calculated using the Doppler effect for electromagnetic waves. The Doppler effect describes the change in frequency observed when there is relative motion between the source of waves and the observer.
Since the space probe is moving towards Earth, the observed frequency will be higher due to the Doppler shift. The formula to calculate the observed frequency (f') is given by:
f' = f / (1 - v/c)
Where:
- f is the original frequency (1.00 GHz)
- v is the speed of the space probe (0.250c)
- c is the speed of light
Plugging in the values we have:
f' = 1.00 GHz / (1 - 0.250) = 1.00 GHz / 0.750 = 1.333 GHz
However, this is not one of the options provided. If this is a typo and the probe was moving away from the Earth, then the received frequency would be:
f' = 1.00 GHz * (1 - 0.250) = 1.00 GHz * 0.750 = 0.750 GHz, which is option b).