time dilated clock
For light, and with the receiver moving at relativistic speeds, clocks on the receiver are time dilated relative to clocks at the source. The receiver will measure the received frequency to be





f

r


=
γ

(

1
−
β

)


f

s


=




1
−
β


1
+
β






f

s


.


{\displaystyle f_{r}=\gamma \left(1-\beta \right)f_{s}={\sqrt {\frac {1-\beta }{1+\beta }}}\,f_{s}.}


where
