bei48482_FM

12 Chapter One

tclonger to reach him than the previous one. Hence the total time between the arrival

of successive waves is

Ttt 0 t 0 t (^0) 
and the observed frequency is
(receding) (^0)  (1.6)
The observed frequency is lower than the source frequency  0. Unlike the case of
sound waves, which propagate relative to a material medium it makes no difference
whether the observer is moving away from the source or the source is moving away
from the observer.
3 Observer approaching the light source. The observer here travels the distance ttoward
the source between ticks, so each light wave takes tcless time to arrive than the
previous one. In this case T t tcand the result is
(approaching) (^0)  (1.7)
1 c

1 c
1 c

1  c
1 c

1  c
1

t 0
1

T
1 c

1  c
 1 c 1 c

 1 c 1 c
1 c

 1 ^2 c^2
t

c
a
4415.1 4526.6
b
The observed frequency is higher than the source frequency. Again, the same formula
holds for motion of the source toward the observer.
Equations (1.6) and (1.7) can be combined in the single formula
 (^0)  (1.8)
by adopting the convention that isfor source and observer approaching each other
andfor source and observer receding from each other.
1 c

1 c
Longitudinal
doppler effect
in light
Spectra of the double star Mizar, which consists of two stars that circle their center of mass, taken
2 days apart. In athe stars are in line with no motion toward or away from the earth, so their
spectral lines are superimposed. In bone star is moving toward the earth and the other is mov-
ing away from the earth, so the spectral lines of the former are doppler-shifted toward the blue
end of the spectrum and those of the latter are shifted toward the red end.
bei48482_ch01.qxd 1/15/02 1:21 AM Page 12