Frequency changes in respect to moving sources and observers

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The discussion focuses on the Doppler effect as it relates to a moving train and its horn frequency. When the train approaches the station, observers hear a higher frequency due to the train's velocity, calculated using f1 = f/(1-(Vs/Vsound)). Conversely, as the train recedes, the frequency decreases, calculated with f1 = f/(1+(Vs/Vsound)). Passengers on the train, moving at the same speed, will hear the original frequency emitted by the horn. This understanding of sound frequency changes is confirmed as accurate.
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I am a little confused about the change in frequencies. I am working on a problem involving a train. The train is moving at a constant velocity and blows its horn at a certain frequency.

I know that the frequency heard by those on the train station will be f1= f/(1-(Vs/Vsound)) when the train is approaching the station where Vs is the constant spead of the train and Vsound is the speed of sound.

I also know that the frequency heard by those on the train station will be f1= f/(1+(Vs/Vsound)) when the train is receding from the station.

However, what is the sound heard by the people on the train. I thinking that as the passengers are moving at the same velocity as the train they would therefore hear the frequency the train was emitting. Is this correct and if not where am I going wrong in my thinking?
 
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This is indeed correct.

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