Here's why:
* The star emits light at a specific frequency. This frequency is determined by the star's composition, temperature, and other physical properties.
* When the star is moving towards the observer, the light waves are compressed. This makes the observed wavelength shorter and the observed frequency higher (blue shift).
* When the star is moving away from the observer, the light waves are stretched. This makes the observed wavelength longer and the observed frequency lower (red shift).
The Doppler effect is a consequence of the wave nature of light and the relative motion between the source and the observer. It does not change the actual frequency of light emitted by the star.
Think of it this way: Imagine a siren on a moving car. The sound of the siren is higher pitched when the car is moving towards you and lower pitched when it's moving away. This is because the sound waves are compressed or stretched due to the car's motion. The Doppler effect works similarly with light waves.
