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

AI Thread Summary
The discussion centers on Ballot's Doppler shift experiment, where a trumpet player on a moving train produces a 463 Hz note, and a stationary trumpeter plays the same note, resulting in 5 beats per second. The speed of sound in air is given as 343 m/s. The initial calculations for the train's speed yield incorrect results, prompting a reevaluation of the frequencies involved. The correct approach involves recognizing that the frequency heard by the listener on the train is higher due to the Doppler effect, leading to the conclusion that the frequencies to consider are 463 Hz and 468 Hz. The thread emphasizes the importance of accurately applying the Doppler shift formula to determine the train's speed.
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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!
 
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Greetings! The formula for beats is fB = 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 = fB + f2.
 
the above post is correct. the frequencies you are looking for are 463 and 468.
 
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