Vl Speed

PHYSICS help..Speeding Train..What is the speed of the train? HELP! 10pts for correct answer?

A person standing close to a railroad crossing hears the whistle of an approaching train. He notes that the pitch of the whistle drops as the train passes by and moves away from the crossing. The frequency of the distant approaching whistle is 548 Hz; it drops to 473 Hz after the train is well past the crossing. What is the speed of the train? Use 340 m/s for the speed of sound in air.

Using the doppler effect you can easily find out the solution of it.
Here the dopper eqnt : n' = ((v - vL)/(v - vS)) * n [here n' denotes the apparent pitch ,
v = speed of the sound ,
vL = speed of the listener ,
vS = speed of the sound source and n denoting the proper pitch ]
( if the source approaches to the listener then vS will be positive neither negative and if the listener approaches to the source vL will be negative neither positive )

so lets solve your task....
1st we counting for the approching whistle :
here vL = 0
v = 340
vS = unknown
n' = 548
n=unknown
so applying dopper effect eqtn we find that

548 = (( v / (v - vS)) * n.........................(1)

now we counting for the whistle crossing pass :
here also vL = 0
v = 340
vS = unknown ( but this speed will appear as negative)
n'=473
n = unknown
so again applying the dopper effect eqtn we find that

473 = (( v / (v + vS ) * n .................................(2)
now dividing eqtn (1) by eqtn (2) we get :

548/473 = ((v + vS)/(v - vS))

now solving the eqtn we get the value of
vS = 24.98
SO THE SPEED OF THE TRAIN WAS 24.98 m/s

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