A sound with frequency fs, is produced by a source traveling along a line with speed vs. If an observer is traveling with speed v0 along the same line from the opposite direction toward the source, then the frequency of the sound heard by the observer is
where c is the speed of sound, about 332 m/s. (This is the Doppler effect.) Suppose that, at a particular moment, you are in a train traveling at 34 m/s and accelerating at 1.2 m/s2. A Train is approaching you from the opposite direction on the other track at 40 m/s. accelerating at 1.4 m/s2 and sounds its whistle, which has a frequency of 460 Hz. At that instant, what is the perceived frequency that you hear and how fast is it changing?
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Multivariable Calculus
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