Question

The Doppler shift was first tested in 1845 by the French scientist B. Ballot. He had a trumpet player sound a 455 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 3 beats/s. How fast was the train moving toward him

Answer 1

Answer:

2.9891

Step-by-step explanation:

Data provided in the question:

Frequency observed by observer, f₀ = 455 Hz

Beats heard by the Ballot = 3 beats/s

Now,

Speed of the sound, V = 343 m/s

Also,

Beats heard = $\left |\frac{f_0\times V}{V-v}-f_0\right|$

here,

v is the speed of the train moving towards the observer

thus,

4 = $\left |\frac{455\times 343}{343-v}-455\right|$

or

$\frac{455\times 343}{343-v}$ = 4 + 455

or

156065 = 459( 343 - v)

or

340.0109 = 343 - v

or

v = 343 - 340.0109

v = 2.9891