B. Ballot had a trumpet player sound an A, 440 Hz, while riding on a flat car pulled by a locomotive..?

Question

at the same time, a stationary trumpeter played the same note. Ballot heard 3.0 beats per second. How fast was the train moving toward him?
- please include how you do it... need help with homework

Answer 1

The beat is the difference in frequencies, so the frequency heard from the trumpeter on the train is 443 Hz. Now, how fast does the train have to be moving in order to Doppler-shift 440 Hz to 443 Hz?

The Doppler Shift equation is

f_observed = f_emitted ( v / ( v - vs ))

where v is the velocity of sound in air and vs is the speed of the train. The velocity of sound in air is about 340 m/s. You know the two frequencies; solve for vs.