A commuter train blows its horn as it passes a passenger platform at a constant speed of 30.0 m/s.

Any help with this is very much appreciated, please try to show work..my class didn't get to go over this chapter because of the tornadoes that hit us.


A commuter train blows its horn as it passes a passenger platform at a constant speed of 30.0 m/s. The train horn sounds at a frequency of 310 Hz when the train is at rest.

(a) What is the frequency observed by a person on the platform as the train approaches?
---- Hz

(b) What is the frequency observed by a person on the platform as the train recedes from him?
---- Hz

(c) What wavelength does the observer find in each case?
---- m
---- m

The first two parts of this problem use the Doppler equation, ƒd = ƒs[(v ± vd)/(v ∓ vs)]

a) The detector is at rest (vd = 0 m/s), and the source is moving towards him at 30.0 m/s.
ƒd = (310 Hz)[(343 m/s + 0)/(343 m/s − 30.0 m/s)] = 339.7 Hz

b) This time, the source is moving away from him.
ƒd = (310 Hz)[(343 m/s + 0)/(343 m/s + 30.0 m/s)] = 285.1 Hz

This makes sense, because one would expect to hear a higher pitched sound as the source approaches the detector, and a lower pitched one as it goes away.

c) v = ƒλ, so:
λ = v/ƒ = (343 m/s)/(339.7) ≈ 1.01 m
λ = v/ƒ = (343 m/s)/(285.1) ≈ 1.20 m