Two trains $A$ and $B$ are moving with speeds $20\ m/s$ and $30\ m/s$ respectively in the same direction on the same straight track, with $B$ ahead of $A$. The engines are at the front ends. The engine of train $A$ blows a long whistle.
Assume that the sound of the whistle is composed of components varying in frequency from $f_{1}=800\ Hz$ to $f_{2}=1120\ Hz$ as shown in the figure. The speed in the frequency (highest frequency lowest frequency) is thus $320\ Hz$. The speed of sound in still air is $340\ m/s$.