A commuter train passes a passenger platform at a constant speed of 31 m/s. The train horn is sounded at its characteristic frequency of 330 Hz.Assume the speed of sound is 343 m/s.

Question

(a) What is the frequency detected by a person on the platform as the train approaches? (b) What frequency is detected by a person on the platform as the train recedes? (c) What overall change in frequency is detected by a person on the plat-form as the train moves from approaching to receding?
(d) What wavelength is detected by a person on the platform as the train approaches?

Answer 1

fo=(1/(1±vs/v))fs

Where the plus sign is negative if the source is approaching the observer and positive if the source is moving away from the observer.

fo is frequency of the observer
fs is the frequency of the source
vs is the speed of the source
v is the speed of sound

a) So as the train approaches,
fs = (1 / (1 - 31/343))*330

b) As the train recedes,
fs = (1 / (1 + 31/343))*330

c) The overall change in frequency is the answer in part a minus the answer in part b

d) The wavelength lamda is given by

lamda = v/f
where v is the speed of sound, and f is the frequency.