Section 14.5 Chain Rule

A sound with frequency \(f_s\) is produced by a source traveling along a line with speed \(v_s\). If an observer is traveling with speed \(v_o\) along the same line from the opposite direction toward the source, then the frequency of the sound heard by the observer is \(f_o = \left(\frac{c + v_o}{c - v_s}\right) f_s\) 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/s\(^2\). A train is approaching you from the opposite direction on the other track at 40 m/s, accelerating at 1.4 m/s\(^2\), 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?