Question

A commuter train passes a passenger platform at a constant speed of 38.1 m/s. The train horn is sounded at its characteristic frequency of 340 Hz.

(a) What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding? (Indicate whether the frequency increases of decreases with the sign of your answer.)
Hz

(b) What wavelength is detected by a person on the platform as the train approaches?
m

Answer 1

A.

Using Doppler's effect

first when train is approaching, which means

Source is moving towards stationary observer, in that case frequency heard by person will be

f1 = f0*V/(V - Vs)

V = Speed of Sound = 343 m/sec

Vs = Speed of Source (train) = 38.1 m/sec

f0 = Characteristic frequency = 340 Hz

So,

f1 = 340*343/(343 - 38.1)

f1 = 382.5 Hz

Now when train is receding, which means

Source is moving away from stationary observer, in that case frequency heard by person will be

f2 = f0*V/(V + Vs)

So,

f2 = 340*343/(343 + 38.1)

f2 = 306.0 Hz

So overall change in frequency will be

Change in frequency = final frequency - Initial frequency

= 306.0 - 382.5

Change in frequency = -76.5 Hz

-ve sign means frequency is decreasing.

Part B.

wavelength is given by:

lambda = Speed of sound/frequency

Now when train is approaching

frequency = f1 = 382.5 Hz

In that case

wavelength = (343 m/sec)/(382.5 Hz) = 0.897 m

Please Upvote.