Doppler Effect

The Doppler shift (sometimes called the Doppler effect) is a change in frequency of emitted waves produced by motion of an emitting source relative to an observer. The Dutch meteorologist Buys-Ballot conducted one of the most famous experiments to confirm the Doppler shift. He put a group of musicians on a train and took up his position on a station platform. He asked the train driver to rush past him as fast as he could while the musicians played and held a constant note, and was able to detect the Doppler shift (as a change in pitch) as the train passed him (Filkin and Hawking 1997, p. 65).

Let the source be in the frame, moving right with velocity towards the stationary frame. Let the observer be in the A frame, moving right with the velocity away from the source,

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