A train is moving parallel and adjacent to a highway with a constant speed of 27

Question

A train is moving parallel and adjacent to
a highway with a constant speed of 27 m/s.
A car is traveling in the same direction as
the train at 47 m/s. The car’s horn sounds
at 510 Hz and the train’s whistle sounds at
340 Hz.
a)When the car is behind the train what fre-
quency does an occupant of the car observe
for the train whistle? The speed of sound is
343 m/s.
Answer in units of Hz

b)When the car is in front of the train what
frequency does a train passenger observe for
the car’s horn?
Answer in units of Hz

Explanation / Answer

Accodring to Doppler effect the observed frequency

                   fobs = fs [ (u± vo) / (u±vs)]
Here fobs isthe frequency observed, fs is the frequency of the source.
u is the speed of the wave, vo is the speed of theobserver, vs is the speed of the source.
If the observer is approaching to the source, use + in thenumerator.
If the observer is going away from the source, use - in thenumerator.
If the source is approaching to the observer, use - in thedenominator.
If the source is going away from the observer, use + in thedenominator.

The speed of sound,u = 343 m/s

-------------------------------------------------------------------------------------------------------------------------

(a) source -- train, observer -- car
the source is going away from the observer and the observer isapproaching to the source
fobs =340 Hz * [(343 m/s + 47 m/s )/(343 m/s + 27 m/s)]

         = 358.4 Hz

(b) source -- car, observer -- train
the source is going away from the observer and the observer isapproaching to the source
fobs = 510 Hz * (343 m/s + 27 m/s )/(343 m/s + 47 m/s)

         = 483.85 Hz

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