Hi,

 It is the observed shift that is varying, not the acatual emitted light. Have you read about the Doppler effect in Sound? It is commonly heard when a vehicle sounding a siren approaches, passes and recedes from an observer. The received frequency is increased (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is decreased during the recession.

For waves that propagate in a medium, such as sound waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted. The total Doppler effect may therefore result from motion of the source, motion of the observer, or motion of the medium. Each of these effects is analyzed separately. For waves which do not require a medium, such as light or gravity in special relativity, only the relative difference in velocity between the observer and the source needs to be considered.

The Doppler effect for electromagnetic waves such as light is of great use in astronomy and results in either a so-called redshift or blue shift. Some galaxies/stars are moving away from the earth so fast that the wavelength of the H alpha-line seems to be increased to 706 nm when we view them from the earth. This is called Redshift since the line has been shifted to the red side of the spectrum. If the galaxy is coming closer to us, we will observe an increase in frequency/ decrease in wavelength (Blue shift). In that case, H alpha line coming from that galaxy could be observed as 400 nm, instead of the terrestrial 656 nm.

It has been used to measure the speed at which stars and galaxies are approaching or receding from us, that is, the radial velocity. This is used to detect if an apparently single star is, in reality, a close binary and even to measure the rotational speed of stars and galaxies.

The use of the Doppler effect for light in astronomy depends on our knowledge that the spectra of stars are not continuous. They exhibit absorption lines at well defined frequencies that are correlated with the energies required to excite electrons in various elements from one level to another. The Doppler effect is recognizable in the fact that the absorption lines are not always at the frequencies that are obtained from the spectrum of a stationary light source. Since blue light has a higher frequency than red light, the spectral lines of an approaching astronomical light source exhibit a blue shift and those of a receding astronomical light source exhibit a redshift.

Among the nearby stars, the largest radial velocities with respect to the Sun are +308 km/s (BD-15°4041, also known as LHS 52, 81.7 light-years away) and -260 km/s (Woolley 9722, also known as Wolf 1106 and LHS 64, 78.2 light-years away). Positive radial velocity means the star is receding from the Sun, negative that it is approaching.

You can read this for more info : http://en.wikipedia.org/wiki/Redshift