A sound frequency detector is on a train moving at constant speed V It approache

Question

A sound frequency detector is on a train moving at constant speed V It approaches a stationary siren that whistles at a standard frequency f. The detector measures a frequency f_1 = 1298 Hz as it moves toward the siren, and a frequency f_2, = 1054 Hz as it moves away from the siren. What is the train speed V? What is the frequency f? now suppose two trains approach each other traveling at the same speed of 40m/s. There is wind of 10 m/s blowing from train A to train B. Each train conductor sounds a whistle with frequency f = 1400Hz, but each hears a different frequency, because of their motion and the wind. What is f_A, the frequency heard by train conductor A?

Explanation / Answer

a)

For moving detector towards the source we use equation,

f' = f*[(v+v0)/v]

Rearranging we get,

f= f’/[(v+v0)/v]------------------(1)

For moving detector away from the source we use equation,

f'’ = f*[(v-v0)/v] ------------------(2)

Plug (1) in (2),

f'’ = { f’/[(v+v0)/v]}*[(v-v0)/v]

1054 = {1298/[(343+v0)/343] }*[(343-v0)/343]

Plugging given values,

v0 = 35.58 m/s

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