(Solved): If a sound with frequency \( f_{s} \) is produced by a source traveling along a line with speed \( ...

If a sound with frequency \( f_{s} \) is produced by a source traveling along a line with speed \( v_{s} \) and 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 \( 332 \mathrm{~m} / \mathrm{s} \). (This is the Doppler effect.) Suppose that, at a particular moment, you are in a train traveling at \( 36 \mathrm{~m} / \mathrm{s} \) and accelerating at \( 1.2 \mathrm{~m} / \mathrm{s}^{2} \). A train is approaching you from the opposite direction on the other track at \( 44 \mathrm{~m} / \mathrm{s} \), accelerating at \( 1.5 \mathrm{~m} / \mathrm{s}^{2} \), and sounds its whistle, which has a frequency of \( 459 \mathrm{~Hz} \). At that instant, what is the perceived frequency that you hear? (Round your answer to one decimal place.) \( \mathrm{Hz} \) How fast is it changing? (Round your answer to two decimal places.) \[ \mathrm{Hz} / \mathrm{s} \]