You stand by the railroad tracks as a train passes by.You hear a 1,100-Hz frequency when the train approaches,which changes to 870 Hz as it goes away.How fast is the train moving? The speed of sound in air is 340 m/s.

Question

Quizplus · Accepted Answer

We can use the formula for the Doppler effect:

f' = f(vs ± vd) / (vs ± vo)

Where:
f = frequency emitted
f' = frequency received
vs = speed of sound 
vd = speed of the detector (train)
vo = speed of the observer (you)

Let's solve for vd:

f1 = 1100 Hz
f2 = 870 Hz
vs = 340 m/s

Using f1:

1100 = f(vs + vd) / (vs + vo)

Using f2:

870 = f(vs - vd) / (vs + vo)

Dividing the equations:

1100/870 = (vs + vd)/(vs - vd)

Simplifying:

vd = vs ((f1 - f2)/(f1 + f2))

Substituting the given values:

vd = 340 ((1100-870)/(1100+870)) = 39.7 m/s

Therefore, the answer is D) 39.7 m/s.

You Stand by the Railroad Tracks as a Train Passes