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speed of sound



A student posed this question, and I have not come up with a definite
answer. Any takers?
A source of sound is moving 343 m/s in air (speed of sound = 345 m/s)
emitting a frequency of 500 Hz. An observer passes the source at a speed of
344 m/s. What will be heard by the observer?
My initial thought was to simply consider the 1 m/s separation of the
source/observer causing a doppler shift reduction in the observed
frequency (498.6 Hz). But, if I consider both of their motions with respect
to the speed of sound I get an observed frequency of 250 Hz. Somebody
straighten me out please!

Darren
watskyd@mail.firn.edu