Doppler effect train frequency question

[Yoruichi]

Homework Statement

When a train running at a speed of 72 km/h approaches a crossing signal, a passenger in the train hears the siren at 720 Hz. What frequency does the passenger detect after the train passes the crossing signal? Take the speed of sound in air to be 340 m/s.

Homework Equations

Doppler effect

The Attempt at a Solution

First I convert the speed of train from 72 km/h into 20 m/s.
Speed of detector = 20 m/s
Speed of source = 0
Speed of sound = 340 m/s
Frequency of source = 720 Hz
Frequency of detector = ?

Using Doppler effect formula:

Fd = (340 - 20) / 340 x 720 (Since the detector is moving away from source, we want to make the denominator greater)
Fd = 677.64 Hz

But this isn't the answer. (The answer is 640 Hz)
May I know which part of my attempt goes wrong?

 

[BvU]

Hello,

At first the train is approaching the crossing. So what the passenger hears is not the frequency of the siren ...

 

[Dr. Courtney]

At first, the train is moving toward the source, so the detected frequency is shifted higher. Is 720 Hz the source frequency or the detected frequency?

When the train moves away from the source, the frequency detected by the train will be lower than the source. Use the true source frequency to compute the detected frequency in this case.

 

[Yoruichi]

Hello,

At first the train is approaching the crossing. So what the passenger hears is not the frequency of the siren ...

At first, the train is moving toward the source, so the detected frequency is shifted higher. Is 720 Hz the source frequency or the detected frequency?

When the train moves away from the source, the frequency detected by the train will be lower than the source. Use the true source frequency to compute the detected frequency in this case.

Oh I see! So the 720 Hz is actually detected frequency instead of source frequency..
Therefore I have to divide my solution into two parts, which is to find out the frequency of detector first, and then only continue with my attempt above!

720 Hz = (340 + 20) / 340 x Fs
Fs = 720 x 340/360
= 680 Hz

Fd = (340 - 20) / 340 x 680
= 640 Hz

Thanks for the clarification!

 

[Dr. Courtney]

Well done!