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
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).