How Fast Was the Train in Ballot's Doppler Shift Experiment?

[bmbradley]

Homework Statement

The Doppler shift was first tested in 1845 by the French scientist B. Ballot. He had a trumpet player sound a 463 Hz note while riding on a flat-car pulled by a locomotive. At the same time, a stationary trumpeter played the same note. Ballot heard 5 beats/s. How fast was the train moving toward him? The speed of sound in air is 343 m/s . Answer in units of m/s.

Homework Equations

f1=(v/(v+vs))f
where f1=463-5=458
v=343 m/s
and f=463

The Attempt at a Solution

458=(343/(343+vs))463
.9892=343/(343+vs)
vs=3.745

I have put in the answer at 3.745 and I also switched f1 and f and got 3.704, but both of those answers are wrong. Please help me figure out what I am doing wrong!

 

[Undoubtedly0]

Greetings! The formula for beats is f_B = f₁ - f₂, where f₁ is the higher frequency. Thus f₁ is the frequency the listener hears from the trumpet on the train, while f₂ is the frequency he hears from the stationary trumpet. Therefore, I believe f₁ = f_B + f₂.

 

[eczeno]

the above post is correct. the frequencies you are looking for are 463 and 468.