Sound frequency of horn 500Hz at 168m/s while in motion at 168Hz?

Question

What is the frequency of the sound of the train horn of 500Hz heard by an observer if a train is approaching the observer at a speed of 168m/s and the observer is moving away (receding) from the train at 168m/s?

please supply formulas.

Answer 1

I'm fairly confident the answer is 500Hz, but i might be miss understanding the question.  The train cannot be approaching the observer if the observer is moving away from the train.  Either the distance between the observer and the train is increase, decreasing or staying the same.

It sounds like what you saying is the distance is staying the same (the train and the observer and moving in the same direction at 168m/s) in which case the 2 Doppler effect's cancel each other out.

However there is still an 168m/s wind observed by the observer and the train.  I dont know who this would effect the frequence by my guess would be, that it would have no effect.  

Find formulas here: http://en.wikipedia.org/wiki/Doppler_eff...

Answer 2

The speed of approach of the train causes a up doppler shift, while the observer's motion causes a down doppler shift.  Understand the principles and you'll see the two equal velocities cancel, so that the frequency heard by the observer and the train operator are the same.

(Imagine the train horn on the back of the train, and you are riding in the front of the same train -- no relative motion, no doppler shift, no formula needed!)

Answer 3

Use the doppler effect

Speed of sound is 340 m/s

fd = 500Hz* (340m/s-168m/s)

                  -------------------------

                  (340 m/s-168m/s)

Go from there.

The numerator subtracts the speed because the observer is moving away and so you want the ratio to be smaller. The denominator subtracts the speed b/c the train is approaching and you want the ratio to be bigger.