Conceptual Doppler Effect question

[jgens]

Homework Statement

A train approaches, and passes through, a station. During this period the velocity of the train is constant and the engine is continuously sounding its whistle. Which one of the following correctly describes what an oberver on the platform will hear?

Sound heard as the train is approaching the station and sound hear as the train is passing through the station.

Homework Equations

N/A

The Attempt at a Solution

Well, my solution was that, given that the perceived velocity of the source is v_scos(theta) it follows that f_p = f₀v_w/(v_w - v_scos(theta)). Hence, the frequency should be decreasing as the train approaches the station since theta -> 90. Additionally I thought that the frequency should be decreasing as the train passes through the station since the expression in the denominator becomes v_w + v_scos(theta) and theta < 90. However, this is not one of the answers supplied with the problem. Would someone mind pointing out where the flaw in my logic is? Thanks.

 

[wywong]

Since the platform is so close to the train, could the question assume theta to be 180 when approaching and 0 after passing?

 

[jgens]

I suppose the question could suppose that, in which case the frequency should be constant as the train approaches and then right as the train passes the observer decrease and remain constant thereafter; however, this still is not one of the options.