Doppler effect: wavelength detected as train approaches at 40 m/s

[TbbZz]

Homework Statement

A train passes a person at a constant speed of 40.0m/s. The train horn is sounded at its characteristic frequency of 320 Hz.

Homework Equations

a) What overall change in frequency is detected by the person as the train moves from approaching to receding?

b) What wavelength is detected by the person as the train approaches?

The Attempt at a Solution

I already solved A. I got a change of -74.2 Hz. 282Hz for approaching and 357.1Hz for receding.

I have absolutely no idea how to do part B. I tried using V = "lambda"f (a.k.a. velocity = wavelength * frequency) but it didn't work.

 

[Chi Meson]

No, you did the right thing. What didi you use for v? The speed of sound, right? (Not the speed of the train, eh?) What numbers did you use and what answer did you get?

 

[TbbZz]

Heh, I was using the speed of the train, thanks for that.

however I'm using the speed of sound for V (345 m/s) and for frequency I'm using 282.9, I'm getting the wrong answer.

 

[hage567]

I think you have your answers for (a) mixed up. As the train approaches the observer the frequency should increase, and as it recedes the frequency should decrease.

Maybe this will help: http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

 

[TbbZz]

I thought if it's approaching, I use +/- and when receding I use -/+

 

[hage567]

I don't know exactly what equation you are using, but I worked it out and I get different answers than you do for (a).
Think of car horn as you are standing on the side of the street. As it comes towards you, it makes a higher pitch than when it moves away from you. So the frequency must increase as it moves towards you for that to happen. Conversely, for the pitch to be lower as it moves away from you, the frequency must decrease.

 

[TbbZz]

What equation am I supposed to be using?

I'm using f1 = f((v + v[observer])/(v - v[source of sound])).

I understand the concept of a higher frequency occurring when you are closer to the source, but the formula just isn't working out that way.

 

[hage567]

That's the right equation for when the train is approaching the observer, with v=345m/s and v[observer]=0. You are solving for f1, right?

I don't know, it works for me!