A commuter train sounds its horn, which has a rest frequency of 500 Hz, as it approaches and then passes a stationary observer standing on an open-air platform. The train travels at a constant speed of 30 m/s through still air in which the speed of sound is 340 m/s.
(a) Qualitatively explain why the frequency heard by the observer while the train approaches must be different from the frequency heard while it recedes. In your explanation, refer explicitly to the direction of the relative velocity between source and observer.
(b) Describe how (and why) the observed frequency varies during the brief instant when the train is directly alongside the observer. Does the frequency equal, exceed, or fall below the rest frequency at that instant? Justify your answer.
(c) Just before the horn is no longer audible, the observer notices that the pitch has dropped by approximately one musical whole step (a decrease of about 12 %). Explain, without performing a numerical calculation, what this observation implies about the sign and magnitude of the relative velocity during that time interval.