Question

A source of electromagnetic radiation is moving in a radial direction relative to you. The frequency you measure is 1.25 times the frequency measured in the rest frame of the source. What is the speed of the source relative to you? Is the source moving toward you or away from you?

Short answer

The speed of the source relative to you is u=0.2195c and the source moving toward me.

Step-by-step solution

Definition of speed

The term speed may be defined as the ratio of distance and time.

Determine the speed of the source relative to you and direction of moving

The given relation is$\mathrm{f}=1.25{\mathrm{f}}_0$

Which shows that$f>f_0$ which is cause thesource moving toward me.

And now the speed can be calculated by the relation is

$$\begin{gathered} u=c\frac{f^2-f_0^2}{f_0^2+f^2} \\ u=c\frac{1.5625f_0^2-f_0^2}{f_0^2+1.5625f_0^2} \\ u=c\frac{1.5625-1}{1+1.5625} \\ u=0.2195c \end{gathered}$$

Hence, the speed of the source relative to you is u=0.2195c and the source moving toward me.