# A confusing problem

As a train APPROACHES a ringing crossing gate, Stacy, a passenger on the train, hears a frequency of 440 Hz from the bell. As the train RECEDES , she hears a frequency of 410 Hz. How fast is the train traveling? (formula: f = fo (v+ vo)/(v-vs))
f= frequency that she hears
fo= actual frequency
v= 330 m/s
vo= observer's frequency
vs= source's frequency
***Solve:
f1= 440 Hz (frequency that she hears as the train approaches the ringing gate)
f2= 410 Hz (frequency that she hears as the train approaches the ringing gate)
vs= 0 m/s
v= 330 m/s
vo=?
vo= [f1(v-vs)]/fo - v
As I got to this point, I was stuck b/c there was no fo, which is the actual frequency, so that I can plug into the equation. plz show me how to do this problem...Thanks

chroot
Staff Emeritus
Gold Member
By symmetry, f0 is obviously halfway between 440 and 410 -- 425 Hz.

- Warren

Alexander
It actually is geometric average: f0=(f1xf2)1/2=424.73 Hz, but here f1 anf f2 are so close that f0 is practically the same as arithmetic average 425 Hz anyway.

Gigi, use the Doppler equation for apparent frequency 2 times (one for approaching train and another for receeding), and you'll get TWO equations with 2 unknown variables (v, f0) - so you can solve for both.

To facilitate work, divide equations one by another and multiply them one by another (this way you'll immediately exclude one or the other unknown).

Last edited by a moderator: