Answer:The velocity of the train is 3.84m/s
Explanation:
According to the Doppler effect, if the source is moving towards you then the apparent frequency of the sound emitted by the source is higher and if the source is moving away from you then the apparent frequency of the sound emitted by the source is smaller.
This is given by:
fo = V +-Vo/ V +-Vo × source
Where fo= observed frequency
V= velocity of sound
Vo= vo it of the observer
fsource= frequency the source
Given:
Observed frequency of the approaching train fo1= 452Hz
The observed frequency of train= fo2= 442Hz
Velocity of sound= 334m/s
Velocity of source=?
Train approaching the observer is given by:
fo1= V/(V - Vs)× source ...eq1
Train passes the student is given by:
fo2= V/(V - Vs)×source ...eq2
Divide eq1 by eq2
452/442 = (343+Vs)/(343 - Vs)
1.02 =(343+Vs)/(343 -Vs)
Cross multiply
1.02(343- Vs) = 343 + Vs
350.76 - 1.02Vs = 343 + Vs
Collecting like terms
350.76 -343= 1.02Vs+ Vs
7.76 = 2.02Vs
Vs= 7.76/2.02
Vs= 3.84m/s
