The Doppler Shift - is this right?

AI Thread Summary
The discussion centers on calculating the speed of a train based on the Doppler shift observed by B. Ballot in 1845. Ballot detected a beat frequency of 3.0 beats per second while comparing the sound of a trumpet played by a stationary musician and one on a moving train. The participant attempted to solve the problem using the formula for the Doppler effect but expressed uncertainty about adding the beat frequency to the original frequency. The calculation resulted in a speed of 2.32 m/s, which the participant questioned. The conversation highlights the complexities of applying the Doppler effect in practical scenarios.
Shiina-kun
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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 an A 440 Hz while riding on a flatcar pulled by a locomotive. 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?


Homework Equations


f' = f/(1-Vs/V)


The Attempt at a Solution



Since it said that Ballot heard 3 bps, I added 3 to 440

443 = 440/(1-Vs/V)
>> 1-Vs/V = 440/443
>> Vs = (440/443 - 1)-V
>> Vs = (440/443 - 1)-343
>> Vs = 2.32 m/s

This doesn't seem right to me. I wasn't really sure if I should have added 3 to 440, but I didn't know how else to find the answer.
 
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It seems ok. The beat frequency is of course given by f_b = |f_2 - f_1|.
 
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