As you stand near a railroad track a train passes by at a sp

As you stand near a railroad track, a train passes by at a speed of 33.7 m/s while sounding its horn at a frequency of 211 Hz. What frequency do you hear as the train approaches you and what frequency while it recedes? Take the speed of sound in air to be 342 m/s.

Solution

f = (v + Vr) f0 / (v + Vs)

v = speed of sound = 342 m/s

Vr = speed of reciever (+ve if moving towards soource) = 0

Vs = speed of source (+ve if moving away)

f0 = frequency of source = 211 Hz

when approaching
Vs = -33.7 m/s

so f = (342 + 0)211 / (342 - 33.7) = 234.06 Hz

when receding

Vs = +33.7 m/s

f = (342 +0)211 / (342 +33.7) = 192.07 Hz