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The doppler effect is a well-known phenomena involving the frequency of radiation received from a source in motion relative to the observer. In the case of sound waves it is manifested by the sound of an approaching vehicle being of higher pitch than a receding one (Look at image below). A very similar effect occurs for light. However, it is simpler in its detail because sound travels in a medium and the velocity of source and observer relative to the medium is important whereas with light only the relative velocity of source and observer matters.

The first direct observation of time dilation was made by Ives and Stilwell in the 1930s. Their experiment basically looked for a transverse doppler shift. If a source is moving towards an observer then the frequency of radiation will be increased whereas if it is moving away from the observer, the frequency will be decreased. These are simple effects related to the lesser or greater distance the light has to travel. However, no such effect is expected at the instant a source is moving past an observer and any frequency shift in those circumstances must represent a fundamental change in the frequency of the source.
The experiment of Ives and Stilwell confirmed the time dilation effect to within about 3%. A modern experiment , using lasers and two photon absorption, agreed with the time dilation factor to within 0.00004
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