A method of distance measurement which reaches much farther than parallax is red shift measurement. People can experience red shift everyday, not only as part of an astronomical phenomenon, but as a related effect called Doppler Shift. Doppler Shift occurs anytime a wave is created by a moving object. For example, when a car is moving down the road and honks its horn, a person standing on the side of the road hears a noise which starts out high pitched and grows lower in pitch as the car passes. Even children notice this effect and often make appropriate noises when playing with toy cars and planes (For an example of how this sounds see http://physics7.berkeley.edu/darkmat/dopplershift.html and click "vroom") The pitch changes because the sound waves pile up upon one another in the direction that the car is moving, causing the frequency of the wave to be higher. This is represented in the following diagram. As the car moves away from the observer the sound waves are stretched out which causes a lowering in pitch.
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