A question about the Doppler efffect

[taculator]

Homework Statement

A commuter train passes a passenger platform at a constant speed of 40 m/s. The train horn is sounded at its characteristic frequency of 320 hz. A) What change in frequency is detected by a person on the platform as the train passes? B) What wavelength is detected by a person on the platform as the train approaches?

Homework Equations

Frequency of detector = (Velocity of Sound+/- Velocity of Detector)/(Velocity of Sound +/- Velocity of Source) times Frequency of Source

The Attempt at a Solution

since the source (train) is moving towards the detector( person on platform) intially i did
Fd= (Vsound)/(Vsound+40) times Fs

where f is frequency
fd is 320 hz
and vsound is 343 m/s

I plugged in and i got that the frequency of the source was 282.7 hz, and then I plugged that into

Fd= (Vsound)/(Vsound-40) times Fs

because that would be the frequency of the detector as the train passes away.
After doing this I found that the change in frequency to be about 84 hz, whereas the answer key said: 75.7 Hz

I know how to solve part B because wavelength= velocity/ frequency but i don't have the correct frequency.


I wasn;t sure whether 320 hertz was the frequency of the detector or the source, so I plugged it into both to solve for the other, but I never ended up getting

 

[denverdoc]

320 is the frequency of the source. Solving for the two frequencies and taking the difference using 340m/s for c I got a somewhat different answer than either yours or the key. Mine was slightly smaller than the keys.

Using the approximation that the shift delta F= -(Vel/c) x f where c= speed of sound.

I get very close to the key's answer. Wavelength is calculated using the formula c=f x lambda where f is the preceived frequency.

 

[taculator]

Ahh i see you used 320 for Fs.

The reason that you got a slightly different answer was because in my book velocity of sound is given as 343 m/s.

The reason I was confused originally is because in the problem it stated "characteristic frequency" so I automatically thought that to be the frequency of the detector, since that can change.

But thank you very much!

 

[denverdoc]

Your welcome. I took characteristic to mean that this was the horn's primary frequency. Usually they are made up of several frequencies but tht is completely beside the point.

BTW, I tried both 340 and 343 and couldn't get the keys answer for total frequency shift using the proper eqns, but who knows may have made a mistake. I believe the answer was in the 73-74 Hz range. Using the approximation I was able to get 75Hz.